Datasets:
all_solutions listlengths 1 38 | answer stringlengths 7 23 | bucket stringclasses 1
value | canonical_solution stringlengths 7 23 | config dict | difficulty stringclasses 1
value | difficulty_proxy float64 -3.64 0 | generator_seed int64 21k 21k | info dict | n_operands int64 4 4 | num_solutions int64 1 38 | operand_range listlengths 2 2 | operands listlengths 4 4 | pass10 dict | problem_id stringlengths 29 29 | question stringlengths 388 392 | split stringclasses 1
value | subset stringclasses 1
value | target int64 10 98 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[
"((1 + 3) * 12)",
"((3 * (1 + 11)) + 12)",
"(((1 + 11) / 3) * 12)",
"((1 + 11) + (3 * 12))",
"((1 + 11) * (12 / 3))",
"(11 + (1 + (3 * 12)))",
"(((1 + 11) * 12) / 3)",
"(1 + (11 + (3 * 12)))"
] | ((3 + 1) * 12) | bucket_a | ((3 + 1) * 12) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.079442 | 21,001 | {
"canonical_solution": "((3 + 1) * 12)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 8 | [
1,
25
] | [
1,
3,
11,
12
] | {
"completion_tokens": 3366,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"parse_error": 3,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00023 | Using the numbers [1, 3, 11, 12], write an arithmetic expression that equals 48.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 48 |
[
"(5 + 25)",
"(((18 - 5) + 25) - 8)",
"((18 + (25 - 5)) - 8)",
"(((18 + 25) - 5) - 8)",
"((18 + 25) - (5 + 8))",
"((25 - 5) + (18 - 8))",
"(25 + ((18 - 5) - 8))",
"(25 + (18 - (5 + 8)))",
"(25 + ((18 - 8) - 5))",
"((18 - 5) + (25 - 8))",
"(18 + ((25 - 5) - 8))",
"(18 + (25 - (5 + 8)))",
"(18 ... | (5 + 25) | bucket_a | (5 + 25) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.772589 | 21,001 | {
"canonical_solution": "(5 + 25)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 16 | [
1,
25
] | [
5,
18,
25,
8
] | {
"completion_tokens": 1971,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 3,
"non_positive_intermediate": 2,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00044 | Using the numbers [5, 18, 25, 8], write an arithmetic expression that equals 30.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 30 |
[
"((5 + 21) + 11)",
"(21 + (5 + 11))",
"(5 + (21 + 11))",
"(((21 - 5) + 11) + 10)",
"((21 + (11 - 5)) + 10)",
"(((21 + 11) - 5) + 10)",
"((21 + 11) + (10 - 5))",
"((11 - 5) + (21 + 10))",
"(11 + ((21 - 5) + 10))",
"(11 + (21 + (10 - 5)))",
"(11 + ((21 + 10) - 5))",
"((21 - 5) + (11 + 10))",
"... | (21 + (5 + 11)) | bucket_a | (21 + (5 + 11)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.890372 | 21,001 | {
"canonical_solution": "(21 + (5 + 11))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"re... | 4 | 18 | [
1,
25
] | [
5,
21,
11,
10
] | {
"completion_tokens": 2938,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"parse_error": 2,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00046 | Using the numbers [5, 21, 11, 10], write an arithmetic expression that equals 37.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 37 |
[
"(7 * 5)",
"((7 + 23) + 5)",
"(23 + (7 + 5))",
"(7 + (23 + 5))",
"((23 + 7) + 5)"
] | (5 * 7) | bucket_a | (5 * 7) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.609438 | 21,001 | {
"canonical_solution": "(5 * 7)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_a... | 4 | 5 | [
1,
25
] | [
7,
23,
7,
5
] | {
"completion_tokens": 2889,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"parse_error": 2,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00055 | Using the numbers [7, 23, 7, 5], write an arithmetic expression that equals 35.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 35 |
[
"(((12 + 6) + 14) + 14)",
"((6 + (12 + 14)) + 14)",
"((12 + (6 + 14)) + 14)",
"((6 + 14) + (12 + 14))",
"((12 + 14) + (6 + 14))",
"(14 + ((12 + 6) + 14))",
"(14 + (6 + (12 + 14)))",
"(14 + (12 + (6 + 14)))",
"((12 + 6) + (14 + 14))",
"(6 + ((12 + 14) + 14))",
"(6 + (14 + (12 + 14)))",
"(6 + (1... | (12 + ((6 + 14) + 14)) | bucket_a | (12 + ((6 + 14) + 14)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "(12 + ((6 + 14) + 14))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
12,
6,
14,
14
] | {
"completion_tokens": 3535,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"parse_error": 3,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00063 | Using the numbers [12, 6, 14, 14], write an arithmetic expression that equals 46.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 46 |
[
"(3 * 24)",
"((24 / 3) * (23 - 14))",
"(24 * ((23 - 14) / 3))",
"((24 * (23 - 14)) / 3)"
] | (3 * 24) | bucket_a | (3 * 24) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.386294 | 21,001 | {
"canonical_solution": "(3 * 24)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 4 | [
1,
25
] | [
3,
23,
24,
14
] | {
"completion_tokens": 3385,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"wrong_value": 5
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00114 | Using the numbers [3, 23, 24, 14], write an arithmetic expression that equals 72.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 72 |
[
"(18 - (11 - (24 - 17)))",
"(18 - (17 - (24 - 11)))",
"(18 - ((17 + 11) - 24))",
"(18 - (24 / (17 - 11)))",
"((24 + 18) - (17 + 11))",
"((24 - 11) + (18 - 17))",
"(((24 - 17) + 18) - 11)",
"(((24 + 18) - 17) - 11)",
"((24 + (18 - 17)) - 11)",
"((24 - 17) + (18 - 11))",
"(((24 - 11) + 18) - 17)",... | ((24 + 18) - (11 + 17)) | bucket_a | ((24 + 18) - (11 + 17)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.772589 | 21,001 | {
"canonical_solution": "((24 + 18) - (11 + 17))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,... | 4 | 16 | [
1,
25
] | [
24,
17,
11,
18
] | {
"completion_tokens": 3908,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"non_positive_intermediate": 3,
"parse_error": 1,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00129 | Using the numbers [24, 17, 11, 18], write an arithmetic expression that equals 14.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as a... | train | easy | 14 |
[
"(6 + (2 * 19))",
"(((2 + 6) + 17) + 19)",
"((6 + (2 + 17)) + 19)",
"((2 + (6 + 17)) + 19)",
"((6 + 17) + (2 + 19))",
"((2 + 17) + (6 + 19))",
"(17 + ((2 + 6) + 19))",
"(17 + (6 + (2 + 19)))",
"(17 + (2 + (6 + 19)))",
"((2 + 6) + (17 + 19))",
"(6 + ((2 + 17) + 19))",
"(6 + (17 + (2 + 19)))",
... | (17 + ((19 + 2) + 6)) | bucket_a | (17 + ((19 + 2) + 6)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.772589 | 21,001 | {
"canonical_solution": "(17 + ((19 + 2) + 6))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 16 | [
1,
25
] | [
2,
6,
17,
19
] | {
"completion_tokens": 5089,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"parse_error": 1,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00134 | Using the numbers [2, 6, 17, 19], write an arithmetic expression that equals 44.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 44 |
[
"(14 + 16)",
"(((23 - 14) + 5) + 16)",
"(((23 + 5) - 14) + 16)",
"((23 - (14 - 5)) + 16)",
"((23 + 16) - (14 - 5))",
"((23 + 5) + (16 - 14))",
"(5 + ((23 - 14) + 16))",
"(5 + ((23 + 16) - 14))",
"(5 + (23 + (16 - 14)))",
"((23 - 14) + (5 + 16))",
"(((23 + 5) + 16) - 14)",
"((5 + (23 + 16)) - 1... | (14 + 16) | bucket_a | (14 + 16) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.772589 | 21,001 | {
"canonical_solution": "(14 + 16)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required... | 4 | 16 | [
1,
25
] | [
23,
14,
5,
16
] | {
"completion_tokens": 2501,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 1,
"non_positive_intermediate": 2,
"parse_error": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00147 | Using the numbers [23, 14, 5, 16], write an arithmetic expression that equals 30.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 30 |
[
"((12 + 8) + 22)",
"(8 + (12 + 22))",
"(12 + (8 + 22))",
"(((12 - 4) * 8) - 22)",
"(((4 * 8) - 12) + 22)",
"((4 * 8) + (22 - 12))",
"((12 / 4) * (22 - 8))",
"((12 * (22 - 8)) / 4)",
"(((4 * 8) + 22) - 12)"
] | ((12 / 4) * (22 - 8)) | bucket_a | ((12 / 4) * (22 - 8)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.197225 | 21,001 | {
"canonical_solution": "((12 / 4) * (22 - 8))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 9 | [
1,
25
] | [
12,
4,
8,
22
] | {
"completion_tokens": 4646,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_integer_intermediate": 1,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00153 | Using the numbers [12, 4, 8, 22], write an arithmetic expression that equals 42.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 42 |
[
"(3 * 24)",
"((5 - 3) * (24 + 12))",
"((24 * (3 + 12)) / 5)",
"(((3 + 5) * 12) - 24)",
"(24 * ((3 * 5) - 12))",
"(24 * ((3 + 12) / 5))"
] | (24 * 3) | bucket_a | (24 * 3) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.791759 | 21,001 | {
"canonical_solution": "(24 * 3)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 6 | [
1,
25
] | [
3,
24,
5,
12
] | {
"completion_tokens": 3845,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"parse_error": 3,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00180 | Using the numbers [3, 24, 5, 12], write an arithmetic expression that equals 72.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 72 |
[
"(25 - 15)",
"(15 - (25 - 20))",
"((20 + 15) - 25)",
"(20 - (25 - 15))",
"(7 + ((20 + 25) / 15))",
"(7 + (15 / (25 - 20)))",
"((7 * (20 - 15)) - 25)",
"((25 * (15 - 7)) / 20)"
] | (((25 + 20) / 15) + 7) | bucket_a | (((25 + 20) / 15) + 7) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.079442 | 21,001 | {
"canonical_solution": "(((25 + 20) / 15) + 7)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 8 | [
1,
25
] | [
20,
25,
7,
15
] | {
"completion_tokens": 3672,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 3,
"non_positive_intermediate": 1,
"parse_error": 1,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00181 | Using the numbers [20, 25, 7, 15], write an arithmetic expression that equals 10.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 10 |
[
"(4 * (11 - 6))",
"(4 * (6 - 1))",
"(((11 - 1) + 4) + 6)",
"(((11 + 4) - 1) + 6)",
"((11 + (4 - 1)) + 6)",
"((1 * 4) * (11 - 6))",
"((4 / 1) * (11 - 6))",
"((4 - 1) + (11 + 6))",
"((11 + 4) + (6 - 1))",
"(4 * ((11 * 1) - 6))",
"(4 * ((11 / 1) - 6))",
"(4 * (1 * (11 - 6)))",
"(4 * ((11 - 6) /... | ((11 + (4 + 6)) - 1) | bucket_a | ((11 + (4 + 6)) - 1) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.295837 | 21,001 | {
"canonical_solution": "((11 + (4 + 6)) - 1)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 27 | [
1,
25
] | [
11,
1,
4,
6
] | {
"completion_tokens": 3732,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 2,
"parse_error": 3,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00183 | Using the numbers [11, 1, 4, 6], write an arithmetic expression that equals 20.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 20 |
[
"((16 + 18) + 18)",
"(18 + (16 + 18))",
"(16 + (18 + 18))",
"(((1 * 16) + 18) + 18)",
"(((16 / 1) + 18) + 18)",
"((16 + (1 * 18)) + 18)",
"((16 + (18 / 1)) + 18)",
"((1 * (16 + 18)) + 18)",
"(((16 + 18) / 1) + 18)",
"((16 + 18) + (1 * 18))",
"((16 + 18) + (18 / 1))",
"((1 * 18) + (16 + 18))",
... | ((18 + 16) + 18) | bucket_a | ((18 + 16) + 18) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.332205 | 21,001 | {
"canonical_solution": "((18 + 16) + 18)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"r... | 4 | 28 | [
1,
25
] | [
1,
16,
18,
18
] | {
"completion_tokens": 2919,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"parse_error": 2,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00189 | Using the numbers [1, 16, 18, 18], write an arithmetic expression that equals 52.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 52 |
[
"(22 - (2 * 5))",
"(24 / 2)",
"(24 - (22 - (2 * 5)))",
"((2 * 5) + (24 - 22))",
"(2 + (5 * (24 - 22)))",
"(((2 * 5) + 24) - 22)"
] | (24 / 2) | bucket_a | (24 / 2) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.791759 | 21,001 | {
"canonical_solution": "(24 / 2)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 6 | [
1,
25
] | [
22,
2,
5,
24
] | {
"completion_tokens": 3353,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"parse_error": 4,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00191 | Using the numbers [22, 2, 5, 24], write an arithmetic expression that equals 12.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 12 |
[
"((5 * 4) + 1)",
"(((5 * 4) - 1) + 2)",
"((4 - 1) * (5 + 2))",
"(((5 * 4) + 2) - 1)",
"((5 * 4) + (2 - 1))"
] | (1 + (4 * 5)) | bucket_a | (1 + (4 * 5)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.609438 | 21,001 | {
"canonical_solution": "(1 + (4 * 5))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"requ... | 4 | 5 | [
1,
25
] | [
5,
4,
1,
2
] | {
"completion_tokens": 2160,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_00199 | Using the numbers [5, 4, 1, 2], write an arithmetic expression that equals 21.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ex... | train | easy | 21 |
[
"(((7 * 2) + 8) + 7)",
"((7 + 8) + (2 * 7))",
"(8 + ((7 * 2) + 7))",
"(8 + (7 + (2 * 7)))",
"((7 * 2) + (8 + 7))",
"(7 + (8 + (2 * 7)))"
] | ((2 * 7) + (7 + 8)) | bucket_a | ((2 * 7) + (7 + 8)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.791759 | 21,001 | {
"canonical_solution": "((2 * 7) + (7 + 8))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 6 | [
1,
25
] | [
7,
2,
8,
7
] | {
"completion_tokens": 4598,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_positive_intermediate": 1,
"parse_error": 3,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00201 | Using the numbers [7, 2, 8, 7], write an arithmetic expression that equals 29.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ex... | train | easy | 29 |
[
"(19 + 17)",
"(((19 + 4) - 4) + 17)",
"(((19 * 4) / 4) + 17)",
"(((19 - 4) + 4) + 17)",
"((4 + (19 - 4)) + 17)",
"((19 * (4 / 4)) + 17)",
"((19 / (4 / 4)) + 17)",
"((4 / 4) * (19 + 17))",
"((19 + 17) / (4 / 4))",
"((19 + 4) + (17 - 4))",
"((19 - 4) + (4 + 17))",
"(((19 + 4) + 17) - 4)",
"((4... | ((4 * (19 + 17)) / 4) | bucket_a | ((4 * (19 + 17)) / 4) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.178054 | 21,001 | {
"canonical_solution": "((4 * (19 + 17)) / 4)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 24 | [
1,
25
] | [
19,
4,
4,
17
] | {
"completion_tokens": 2115,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"parse_error": 1,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00213 | Using the numbers [19, 4, 4, 17], write an arithmetic expression that equals 36.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 36 |
[
"(13 - 2)",
"((13 * 2) - 15)",
"((2 + 15) - 6)",
"(15 - (6 - 2))",
"(2 + (15 - 6))",
"(((2 * 15) - 13) - 6)",
"((2 * 15) - (13 + 6))",
"(((13 + 15) - 6) / 2)",
"((15 + (13 - 6)) / 2)",
"((13 + (15 - 6)) / 2)",
"(((2 * 15) - 6) - 13)"
] | ((2 + 15) - 6) | bucket_a | ((2 + 15) - 6) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.397895 | 21,001 | {
"canonical_solution": "((2 + 15) - 6)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 11 | [
1,
25
] | [
13,
2,
15,
6
] | {
"completion_tokens": 3433,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_positive_intermediate": 1,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00231 | Using the numbers [13, 2, 15, 6], write an arithmetic expression that equals 11.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 11 |
[
"((15 + 11) + 24)",
"(11 + (15 + 24))",
"(15 + (11 + 24))",
"(((15 - 11) + 24) + 22)",
"(((15 + 24) - 11) + 22)",
"((15 + (24 - 11)) + 22)",
"((24 - 11) + (15 + 22))",
"((15 + 24) + (22 - 11))",
"(24 + ((15 - 11) + 22))",
"(24 + ((15 + 22) - 11))",
"(24 + (15 + (22 - 11)))",
"((15 - 11) + (24 ... | ((15 + (24 - 11)) + 22) | bucket_a | ((15 + (24 - 11)) + 22) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.890372 | 21,001 | {
"canonical_solution": "((15 + (24 - 11)) + 22)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,... | 4 | 18 | [
1,
25
] | [
15,
11,
24,
22
] | {
"completion_tokens": 3454,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"parse_error": 2,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00235 | Using the numbers [15, 11, 24, 22], write an arithmetic expression that equals 50.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as a... | train | easy | 50 |
[
"((13 * 2) + 25)",
"((2 * 25) + 1)",
"(((13 * 2) + 25) * 1)",
"(((13 * 2) + 25) / 1)",
"(25 + ((13 * 2) * 1))",
"(25 + ((13 * 2) / 1))",
"(25 + (2 * (13 * 1)))",
"(25 + (2 * (13 / 1)))",
"(25 + (13 * (2 * 1)))",
"(25 + (13 * (2 / 1)))",
"((13 * 2) + (25 * 1))",
"((13 * 2) + (25 / 1))"
] | ((25 * 1) + (2 * 13)) | bucket_a | ((25 * 1) + (2 * 13)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.484907 | 21,001 | {
"canonical_solution": "((25 * 1) + (2 * 13))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 12 | [
1,
25
] | [
13,
2,
25,
1
] | {
"completion_tokens": 3448,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 1,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00240 | Using the numbers [13, 2, 25, 1], write an arithmetic expression that equals 51.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 51 |
[
"(2 + 13)",
"((3 + 2) * 3)",
"(3 * (2 + 3))",
"(((3 + 2) + 13) - 3)",
"((2 + (3 + 13)) - 3)",
"((3 + (2 + 13)) - 3)",
"((13 - (3 - 2)) + 3)",
"((2 + (13 - 3)) + 3)",
"(((2 + 13) - 3) + 3)",
"(((13 - 3) / 2) * 3)",
"(((2 + 13) / 3) * 3)",
"((3 * (2 + 13)) / 3)",
"((2 + 13) * (3 / 3))",
"((2... | ((13 + 2) / (3 / 3)) | bucket_a | ((13 + 2) / (3 / 3)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.332205 | 21,001 | {
"canonical_solution": "((13 + 2) / (3 / 3))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 28 | [
1,
25
] | [
3,
2,
13,
3
] | {
"completion_tokens": 2697,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"parse_error": 2,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00243 | Using the numbers [3, 2, 13, 3], write an arithmetic expression that equals 15.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 15 |
[
"(((19 + 24) - 13) + 9)",
"((24 + (19 - 13)) + 9)",
"((19 + (24 - 13)) + 9)",
"((24 - 13) + (19 + 9))",
"((19 - 13) + (24 + 9))",
"(((19 + 24) + 9) - 13)",
"((24 + (19 + 9)) - 13)",
"((19 + (24 + 9)) - 13)",
"((19 + 24) - (13 - 9))",
"(24 + ((19 - 13) + 9))",
"(24 + ((19 + 9) - 13))",
"(24 + (... | ((19 - (13 - 9)) + 24) | bucket_a | ((19 - (13 - 9)) + 24) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((19 - (13 - 9)) + 24)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
19,
24,
13,
9
] | {
"completion_tokens": 2615,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"parse_error": 2,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00251 | Using the numbers [19, 24, 13, 9], write an arithmetic expression that equals 39.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 39 |
[
"((4 + 14) + 8)",
"(14 + (4 + 8))",
"(4 + (14 + 8))",
"(((14 - 4) + 8) + 8)",
"(((4 * 8) - 14) + 8)",
"((14 + (8 - 4)) + 8)",
"(((14 + 8) - 4) + 8)",
"((14 + 8) + (8 - 4))",
"((4 * 8) - (14 - 8))",
"((8 - 4) + (14 + 8))",
"(8 + ((14 - 4) + 8))",
"(8 + ((4 * 8) - 14))",
"(8 + (14 + (8 - 4)))"... | ((8 * 4) - (14 - 8)) | bucket_a | ((8 * 4) - (14 - 8)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.178054 | 21,001 | {
"canonical_solution": "((8 * 4) - (14 - 8))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 24 | [
1,
25
] | [
4,
14,
8,
8
] | {
"completion_tokens": 1766,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"parse_error": 3,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00257 | Using the numbers [4, 14, 8, 8], write an arithmetic expression that equals 26.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 26 |
[
"(((17 - 9) + 8) + 4)",
"(((17 + 8) - 9) + 4)",
"((17 - (9 - 8)) + 4)",
"((17 + 4) - (9 - 8))",
"((17 + 8) - (9 - 4))",
"(8 + ((17 - 9) + 4))",
"(8 + ((17 + 4) - 9))",
"(8 + (17 - (9 - 4)))",
"((17 - 9) + (8 + 4))",
"(((17 + 8) + 4) - 9)",
"((8 + (17 + 4)) - 9)",
"((17 + (8 + 4)) - 9)",
"(17... | ((17 - 9) + (8 + 4)) | bucket_a | ((17 - 9) + (8 + 4)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((17 - 9) + (8 + 4))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
17,
9,
8,
4
] | {
"completion_tokens": 5169,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 2,
"no_box": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00258 | Using the numbers [17, 9, 8, 4], write an arithmetic expression that equals 20.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 20 |
[
"(13 + 22)",
"(((13 + 22) + 7) - 7)",
"((22 + (13 + 7)) - 7)",
"((13 + (22 + 7)) - 7)",
"(((13 + 22) * 7) / 7)",
"(((13 + 22) - 7) + 7)",
"((22 + (13 - 7)) + 7)",
"((13 + (22 - 7)) + 7)",
"(((13 + 22) / 7) * 7)",
"((22 + 7) + (13 - 7))",
"((22 - 7) + (13 + 7))",
"((13 + 7) + (22 - 7))",
"((1... | (((7 + 13) + 22) - 7) | bucket_a | (((7 + 13) + 22) - 7) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.258097 | 21,001 | {
"canonical_solution": "(((7 + 13) + 22) - 7)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 26 | [
1,
25
] | [
13,
22,
7,
7
] | {
"completion_tokens": 3161,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"parse_error": 3,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00264 | Using the numbers [13, 22, 7, 7], write an arithmetic expression that equals 35.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 35 |
[
"(2 + 14)",
"((4 - 2) + 14)",
"((4 / 2) + 14)",
"((4 + 14) - 2)",
"(4 + (14 - 2))",
"(2 * 8)",
"((4 * 2) + 8)",
"((4 - 2) * 8)",
"((4 / 2) * 8)",
"((4 * 8) / 2)",
"(4 * (8 / 2))",
"(14 + (8 / 4))",
"((14 - (4 + 2)) + 8)",
"(((14 - 4) - 2) + 8)",
"(((14 - 2) - 4) + 8)",
"(((2 * 14) - 4)... | (8 + (14 - (4 + 2))) | bucket_a | (8 + (14 - (4 + 2))) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.610918 | 21,001 | {
"canonical_solution": "(8 + (14 - (4 + 2)))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 37 | [
1,
25
] | [
4,
2,
14,
8
] | {
"completion_tokens": 2568,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_00270 | Using the numbers [4, 2, 14, 8], write an arithmetic expression that equals 16.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 16 |
[
"(23 - (7 + 4))",
"((23 - 7) - 4)",
"((23 - 4) - 7)",
"((7 - 4) * 4)",
"(4 * (7 - 4))"
] | ((23 - 7) - 4) | bucket_a | ((23 - 7) - 4) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.609438 | 21,001 | {
"canonical_solution": "((23 - 7) - 4)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 5 | [
1,
25
] | [
7,
4,
23,
4
] | {
"completion_tokens": 2592,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_positive_intermediate": 1,
"parse_error": 2,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00280 | Using the numbers [7, 4, 23, 4], write an arithmetic expression that equals 12.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 12 |
[
"(1 + 15)",
"((21 - (19 + 1)) + 15)",
"(((21 - 19) - 1) + 15)",
"(((21 - 1) - 19) + 15)",
"((21 - 1) - (19 - 15))",
"((21 - 19) + (15 - 1))",
"(21 - ((19 + 1) - 15))",
"(21 - (1 + (19 - 15)))",
"(21 - (19 - (15 - 1)))",
"((21 + 15) - (19 + 1))",
"(((21 - 19) + 15) - 1)",
"((21 - (19 - 15)) - 1... | (15 + 1) | bucket_a | (15 + 1) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.772589 | 21,001 | {
"canonical_solution": "(15 + 1)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 16 | [
1,
25
] | [
19,
1,
21,
15
] | {
"completion_tokens": 1610,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"parse_error": 2,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00281 | Using the numbers [19, 1, 21, 15], write an arithmetic expression that equals 16.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 16 |
[
"22",
"((14 + 22) - 14)",
"((14 * 22) / 14)",
"((22 - 14) + 14)",
"(22 * (14 / 14))",
"(22 / (14 / 14))",
"((22 + 14) - 14)",
"((22 * 14) / 14)",
"(14 + (22 - 14))",
"((14 + 14) - 6)",
"(14 + (14 - 6))"
] | (14 + (22 - 14)) | bucket_a | (14 + (22 - 14)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.397895 | 21,001 | {
"canonical_solution": "(14 + (22 - 14))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"r... | 4 | 11 | [
1,
25
] | [
14,
22,
14,
6
] | {
"completion_tokens": 3307,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"parse_error": 2,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00285 | Using the numbers [14, 22, 14, 6], write an arithmetic expression that equals 22.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 22 |
[
"((13 - 1) + 6)",
"(13 + (6 - 1))",
"((13 + 6) - 1)",
"((1 + 6) + 11)",
"(6 + (1 + 11))",
"(1 + (6 + 11))",
"((13 - 6) + 11)",
"((13 + 11) - 6)",
"(13 + (11 - 6))",
"(((1 * 13) - 6) + 11)",
"(((13 / 1) - 6) + 11)",
"((13 - (1 * 6)) + 11)",
"((13 - (6 / 1)) + 11)",
"((1 * (13 - 6)) + 11)",
... | (((13 + 11) - 6) / 1) | bucket_a | (((13 + 11) - 6) / 1) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.526361 | 21,001 | {
"canonical_solution": "(((13 + 11) - 6) / 1)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 34 | [
1,
25
] | [
1,
13,
6,
11
] | {
"completion_tokens": 2329,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_positive_intermediate": 1,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00292 | Using the numbers [1, 13, 6, 11], write an arithmetic expression that equals 18.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 18 |
[
"(8 + (9 * 7))",
"((8 * 8) + 7)",
"(((9 * 8) - 8) + 7)",
"((9 * 8) - (8 - 7))",
"(((9 * 8) + 7) - 8)"
] | (8 + (7 * 9)) | bucket_a | (8 + (7 * 9)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.609438 | 21,001 | {
"canonical_solution": "(8 + (7 * 9))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"requ... | 4 | 5 | [
1,
25
] | [
9,
8,
8,
7
] | {
"completion_tokens": 4742,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"parse_error": 3,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00307 | Using the numbers [9, 8, 8, 7], write an arithmetic expression that equals 71.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ex... | train | easy | 71 |
[
"(20 - (9 - (13 - 5)))",
"(20 - ((5 + 9) - 13))",
"(20 - (5 - (13 - 9)))",
"((13 - 9) + (20 - 5))",
"((13 + 20) - (5 + 9))",
"(((13 - 5) + 20) - 9)",
"((13 + (20 - 5)) - 9)",
"(((13 + 20) - 5) - 9)",
"((13 - 5) + (20 - 9))",
"(13 + (20 - (5 + 9)))",
"(13 + ((20 - 5) - 9))",
"(13 + ((20 - 9) - ... | ((13 - 9) + (20 - 5)) | bucket_a | ((13 - 9) + (20 - 5)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((13 - 9) + (20 - 5))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
5,
13,
9,
20
] | {
"completion_tokens": 3627,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"invalid_operands": 2,
"parse_error": 1,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_00309 | Using the numbers [5, 13, 9, 20], write an arithmetic expression that equals 19.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 19 |
[
"(((6 * 18) - 15) - 6)",
"((6 * 18) - (15 + 6))",
"((15 * 6) - (18 / 6))",
"((18 * 6) - (15 + 6))",
"(((18 * 6) - 15) - 6)",
"(((6 * 18) - 6) - 15)",
"(((18 * 6) - 6) - 15)",
"(15 + ((18 - 6) * 6))",
"(15 + (6 * (18 - 6)))"
] | ((6 * 18) - (6 + 15)) | bucket_a | ((6 * 18) - (6 + 15)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.197225 | 21,001 | {
"canonical_solution": "((6 * 18) - (6 + 15))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 9 | [
1,
25
] | [
15,
6,
18,
6
] | {
"completion_tokens": 6437,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 2,
"non_positive_intermediate": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00325 | Using the numbers [15, 6, 18, 6], write an arithmetic expression that equals 87.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 87 |
[
"(1 + 19)",
"((2 - 1) + 19)",
"((2 + 19) - 1)",
"(2 + (19 - 1))",
"(2 + 18)",
"((2 * 1) + 18)",
"((2 / 1) + 18)",
"(1 * (2 + 18))",
"((2 + 18) / 1)",
"(2 + (1 * 18))",
"(2 + (18 / 1))",
"((2 * 19) - 18)",
"(((2 * 1) * 19) - 18)",
"(((2 / 1) * 19) - 18)",
"((1 * (2 * 19)) - 18)",
"(((2 ... | (18 + 2) | bucket_a | (18 + 2) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.091042 | 21,001 | {
"canonical_solution": "(18 + 2)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 22 | [
1,
25
] | [
2,
1,
19,
18
] | {
"completion_tokens": 2884,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"parse_error": 3,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00329 | Using the numbers [2, 1, 19, 18], write an arithmetic expression that equals 20.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 20 |
[
"((23 + (6 * 9)) + 6)",
"((6 * 9) + (23 + 6))",
"((23 + 6) + (9 * 6))",
"(6 + (23 + (9 * 6)))",
"(23 + ((6 * 9) + 6))",
"(23 + (6 + (9 * 6)))"
] | (((9 * 6) + 23) + 6) | bucket_a | (((9 * 6) + 23) + 6) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.791759 | 21,001 | {
"canonical_solution": "(((9 * 6) + 23) + 6)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 6 | [
1,
25
] | [
23,
6,
9,
6
] | {
"completion_tokens": 5406,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 4,
"parse_error": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00331 | Using the numbers [23, 6, 9, 6], write an arithmetic expression that equals 83.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 83 |
[
"((19 * 4) - 23)",
"(((23 + 7) + 19) + 4)",
"((7 + (23 + 19)) + 4)",
"((23 + (7 + 19)) + 4)",
"((7 + 19) + (23 + 4))",
"((23 + 19) + (7 + 4))",
"(19 + ((23 + 7) + 4))",
"(19 + (7 + (23 + 4)))",
"(19 + (23 + (7 + 4)))",
"((23 + 7) + (19 + 4))",
"(7 + ((23 + 19) + 4))",
"(7 + (19 + (23 + 4)))",
... | ((19 + 4) + (7 + 23)) | bucket_a | ((19 + 4) + (7 + 23)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.772589 | 21,001 | {
"canonical_solution": "((19 + 4) + (7 + 23))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 16 | [
1,
25
] | [
23,
7,
19,
4
] | {
"completion_tokens": 2538,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_00350 | Using the numbers [23, 7, 19, 4], write an arithmetic expression that equals 53.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 53 |
[
"(18 + 25)",
"((15 + 25) + (18 / 6))",
"(25 + ((18 - 15) * 6))",
"(25 + (15 + (18 / 6)))",
"(15 + (25 + (18 / 6)))"
] | (18 + 25) | bucket_a | (18 + 25) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.609438 | 21,001 | {
"canonical_solution": "(18 + 25)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required... | 4 | 5 | [
1,
25
] | [
15,
18,
25,
6
] | {
"completion_tokens": 4898,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"non_positive_intermediate": 1,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00353 | Using the numbers [15, 18, 25, 6], write an arithmetic expression that equals 43.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 43 |
[
"(((22 + 10) + 4) + 7)",
"((10 + (22 + 4)) + 7)",
"((22 + (10 + 4)) + 7)",
"((10 + 4) + (22 + 7))",
"((22 + 4) + (10 + 7))",
"(4 + ((22 + 10) + 7))",
"(4 + (10 + (22 + 7)))",
"(4 + (22 + (10 + 7)))",
"((22 + 10) + (4 + 7))",
"(10 + ((22 + 4) + 7))",
"(10 + (4 + (22 + 7)))",
"(10 + (22 + (4 + 7... | ((22 + 4) + (10 + 7)) | bucket_a | ((22 + 4) + (10 + 7)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((22 + 4) + (10 + 7))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
22,
10,
4,
7
] | {
"completion_tokens": 3561,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"no_box": 1,
"parse_error": 3,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00399 | Using the numbers [22, 10, 4, 7], write an arithmetic expression that equals 43.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 43 |
[
"(23 - (18 - (24 - 16)))",
"(23 - (16 - (24 - 18)))",
"(23 - ((16 + 18) - 24))",
"((24 + 23) - (16 + 18))",
"((24 - 18) + (23 - 16))",
"(((24 - 16) + 23) - 18)",
"(((24 + 23) - 16) - 18)",
"((24 + (23 - 16)) - 18)",
"((24 - 16) + (23 - 18))",
"(((24 - 18) + 23) - 16)",
"(((24 + 23) - 18) - 16)",... | (((24 + 23) - 16) - 18) | bucket_a | (((24 + 23) - 16) - 18) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "(((24 + 23) - 16) - 18)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,... | 4 | 15 | [
1,
25
] | [
24,
16,
18,
23
] | {
"completion_tokens": 2221,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"non_positive_intermediate": 4,
"parse_error": 1
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00401 | Using the numbers [24, 16, 18, 23], write an arithmetic expression that equals 13.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as a... | train | easy | 13 |
[
"(22 - (14 - 12))",
"((12 + 22) - 14)",
"(12 + (22 - 14))",
"(22 - (24 / 12))",
"(24 - ((12 + 14) - 22))",
"(24 - (14 - (22 - 12)))",
"(24 - (12 - (22 - 14)))",
"(((14 - 12) * 22) - 24)",
"((14 * 22) - (12 * 24))",
"((22 - 14) + (24 - 12))",
"((22 - 12) + (24 - 14))",
"(22 - ((12 + 14) - 24))"... | (24 - (14 - (22 - 12))) | bucket_a | (24 - (14 - (22 - 12))) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.091042 | 21,001 | {
"canonical_solution": "(24 - (14 - (22 - 12)))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,... | 4 | 22 | [
1,
25
] | [
12,
14,
22,
24
] | {
"completion_tokens": 3922,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 4,
"parse_error": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00410 | Using the numbers [12, 14, 22, 24], write an arithmetic expression that equals 20.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as a... | train | easy | 20 |
[
"((15 + 17) + 24)",
"(17 + (15 + 24))",
"(15 + (17 + 24))",
"((15 - 7) * (24 - 17))",
"(7 * ((15 + 17) - 24))",
"(7 * (17 - (24 - 15)))",
"(7 * (15 - (24 - 17)))"
] | ((15 + 17) + 24) | bucket_a | ((15 + 17) + 24) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.94591 | 21,001 | {
"canonical_solution": "((15 + 17) + 24)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"r... | 4 | 7 | [
1,
25
] | [
7,
15,
17,
24
] | {
"completion_tokens": 3515,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"non_positive_intermediate": 1,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00423 | Using the numbers [7, 15, 17, 24], write an arithmetic expression that equals 56.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 56 |
[
"(((19 + 19) + 17) + 16)",
"((19 + (19 + 17)) + 16)",
"((19 + 17) + (19 + 16))",
"(17 + ((19 + 19) + 16))",
"(17 + (19 + (19 + 16)))",
"((19 + 19) + (17 + 16))",
"(19 + ((19 + 17) + 16))",
"(19 + (17 + (19 + 16)))",
"(19 + (19 + (17 + 16)))"
] | (17 + (19 + (16 + 19))) | bucket_a | (17 + (19 + (16 + 19))) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.197225 | 21,001 | {
"canonical_solution": "(17 + (19 + (16 + 19)))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,... | 4 | 9 | [
1,
25
] | [
19,
19,
17,
16
] | {
"completion_tokens": 4241,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 3,
"non_positive_intermediate": 1,
"parse_error": 1
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00435 | Using the numbers [19, 19, 17, 16], write an arithmetic expression that equals 71.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as a... | train | easy | 71 |
[
"(((23 - 9) + 14) + 25)",
"(((23 + 14) - 9) + 25)",
"((23 + (14 - 9)) + 25)",
"((14 - 9) + (23 + 25))",
"((23 + 14) + (25 - 9))",
"(14 + ((23 - 9) + 25))",
"(14 + ((23 + 25) - 9))",
"(14 + (23 + (25 - 9)))",
"((23 - 9) + (14 + 25))",
"(((23 + 14) + 25) - 9)",
"((14 + (23 + 25)) - 9)",
"((23 + ... | (((23 + 14) - 9) + 25) | bucket_a | (((23 + 14) - 9) + 25) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "(((23 + 14) - 9) + 25)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
23,
9,
14,
25
] | {
"completion_tokens": 4711,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 2,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00439 | Using the numbers [23, 9, 14, 25], write an arithmetic expression that equals 53.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 53 |
[
"(15 + 13)",
"((23 - 9) * (15 - 13))"
] | ((23 - 9) * (15 - 13)) | bucket_a | ((23 - 9) * (15 - 13)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -0.693147 | 21,001 | {
"canonical_solution": "((23 - 9) * (15 - 13))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 2 | [
1,
25
] | [
9,
23,
15,
13
] | {
"completion_tokens": 3463,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"invalid_operands": 1,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_00459 | Using the numbers [9, 23, 15, 13], write an arithmetic expression that equals 28.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 28 |
[
"(15 * 4)",
"((15 * 4) * 1)",
"((15 * 4) / 1)",
"(4 * (15 * 1))",
"(4 * (15 / 1))",
"(15 * (4 * 1))",
"(15 * (4 / 1))",
"((15 * (15 + 1)) / 4)",
"(15 * ((15 + 1) / 4))",
"((15 * (4 + 1)) - 15)",
"(15 + (15 * (4 - 1)))"
] | (4 * 15) | bucket_a | (4 * 15) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.397895 | 21,001 | {
"canonical_solution": "(4 * 15)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 11 | [
1,
25
] | [
15,
15,
4,
1
] | {
"completion_tokens": 2904,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"non_positive_intermediate": 1,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00467 | Using the numbers [15, 15, 4, 1], write an arithmetic expression that equals 60.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 60 |
[
"(14 + 2)",
"((14 - 6) * 2)",
"(2 * (14 - 6))",
"(((14 + 6) + 2) - 6)",
"((6 + (14 + 2)) - 6)",
"(((14 * 2) - 6) - 6)",
"((14 + (6 + 2)) - 6)",
"(((14 + 6) / 2) + 6)",
"(((14 - 6) + 2) + 6)",
"(((14 + 2) - 6) + 6)",
"((14 - (6 - 2)) + 6)",
"((6 * (14 + 2)) / 6)",
"((6 + 2) + (14 - 6))",
"(... | (2 + 14) | bucket_a | (2 + 14) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.332205 | 21,001 | {
"canonical_solution": "(2 + 14)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 28 | [
1,
25
] | [
14,
6,
2,
6
] | {
"completion_tokens": 2603,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"wrong_value": 6
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00480 | Using the numbers [14, 6, 2, 6], write an arithmetic expression that equals 16.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 16 |
[
"22",
"(((5 + 10) + 22) - 15)",
"((10 + (5 + 22)) - 15)",
"((5 + (10 + 22)) - 15)",
"(((5 + 10) * 22) / 15)",
"((22 - (5 + 10)) + 15)",
"(((22 - 5) - 10) + 15)",
"(((22 - 10) - 5) + 15)",
"((10 + 22) - (15 - 5))",
"((10 * 22) / (15 - 5))",
"((22 - 10) + (15 - 5))",
"((5 + 22) - (15 - 10))",
... | (22 / (15 / (10 + 5))) | bucket_a | (22 / (15 / (10 + 5))) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.258097 | 21,001 | {
"canonical_solution": "(22 / (15 / (10 + 5)))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 26 | [
1,
25
] | [
5,
10,
22,
15
] | {
"completion_tokens": 1925,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_integer_intermediate": 1,
"non_positive_intermediate": 1,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00504 | Using the numbers [5, 10, 22, 15], write an arithmetic expression that equals 22.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 22 |
[
"((5 + 15) + 4)",
"(15 + (5 + 4))",
"(5 + (15 + 4))",
"((5 * 4) + 4)",
"(4 + (5 * 4))",
"(((15 - 5) - 4) * 4)",
"((15 - (5 + 4)) * 4)",
"(((15 - 4) - 5) * 4)",
"(4 * ((15 - 5) - 4))",
"(4 * (15 - (5 + 4)))",
"(4 * ((15 - 4) - 5))",
"((15 / 5) * (4 + 4))",
"((15 * (4 + 4)) / 5)"
] | (5 + (4 + 15)) | bucket_a | (5 + (4 + 15)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.564949 | 21,001 | {
"canonical_solution": "(5 + (4 + 15))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 13 | [
1,
25
] | [
5,
15,
4,
4
] | {
"completion_tokens": 3679,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_integer_intermediate": 1,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00516 | Using the numbers [5, 15, 4, 4], write an arithmetic expression that equals 24.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 24 |
[
"(3 + 7)",
"((9 / 3) + 7)",
"(9 + (3 / 3))",
"(7 + 3)",
"(7 + (9 / 3))",
"(((9 - 3) + 7) - 3)",
"((9 + (7 - 3)) - 3)",
"(((9 + 7) - 3) - 3)",
"((9 + (3 * 7)) / 3)",
"((9 + 7) - (3 + 3))",
"((7 - 3) + (9 - 3))",
"(7 + ((9 - 3) - 3))",
"(7 + (9 - (3 + 3)))",
"((9 - 3) + (7 - 3))",
"(9 + ((... | (((9 - 3) - 3) + 7) | bucket_a | (((9 - 3) - 3) + 7) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.890372 | 21,001 | {
"canonical_solution": "(((9 - 3) - 3) + 7)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 18 | [
1,
25
] | [
3,
9,
7,
3
] | {
"completion_tokens": 2747,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"invalid_operands": 1,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_00519 | Using the numbers [3, 9, 7, 3], write an arithmetic expression that equals 10.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ex... | train | easy | 10 |
[
"(17 + 20)",
"(((18 + 17) + 22) - 20)",
"((17 + (18 + 22)) - 20)",
"((18 + (17 + 22)) - 20)",
"((17 + 22) - (20 - 18))",
"((18 + 22) - (20 - 17))",
"(22 + ((18 + 17) - 20))",
"(22 + (17 - (20 - 18)))",
"(22 + (18 - (20 - 17)))",
"((18 + 17) + (22 - 20))",
"(17 + ((18 + 22) - 20))",
"(17 + (22 ... | (20 + 17) | bucket_a | (20 + 17) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.772589 | 21,001 | {
"canonical_solution": "(20 + 17)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required... | 4 | 16 | [
1,
25
] | [
18,
17,
22,
20
] | {
"completion_tokens": 2394,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"parse_error": 1,
"wrong_value": 5
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00521 | Using the numbers [18, 17, 22, 20], write an arithmetic expression that equals 37.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as a... | train | easy | 37 |
[
"(6 * (5 + 5))",
"(5 * 12)",
"(((6 - 5) * 5) * 12)",
"((5 / (6 - 5)) * 12)",
"((6 - (5 / 5)) * 12)",
"((5 * (6 - 5)) * 12)",
"((6 - 5) * (5 * 12))",
"((5 * 12) / (6 - 5))",
"((5 + 5) * (12 - 6))",
"(5 * ((6 - 5) * 12))",
"(5 * (12 / (6 - 5)))"
] | (12 * 5) | bucket_a | (12 * 5) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.397895 | 21,001 | {
"canonical_solution": "(12 * 5)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 11 | [
1,
25
] | [
5,
6,
5,
12
] | {
"completion_tokens": 2989,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"wrong_value": 5
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00522 | Using the numbers [5, 6, 5, 12], write an arithmetic expression that equals 60.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 60 |
[
"18",
"((18 / 6) + 15)",
"(6 * (18 - 15))",
"(21 - (18 / 6))",
"(6 * (21 - 18))",
"(21 - (18 - 15))",
"(15 + (21 - 18))",
"((15 + 21) - 18)",
"(((6 + 18) + 15) - 21)",
"((18 + (6 + 15)) - 21)",
"((6 + (18 + 15)) - 21)",
"(21 - (15 - (18 - 6)))",
"(21 - ((6 + 15) - 18))",
"(21 - (6 - (18 - ... | ((15 - (21 - 18)) + 6) | bucket_a | ((15 - (21 - 18)) + 6) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.496508 | 21,001 | {
"canonical_solution": "((15 - (21 - 18)) + 6)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 33 | [
1,
25
] | [
6,
18,
15,
21
] | {
"completion_tokens": 2441,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_positive_intermediate": 1,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00526 | Using the numbers [6, 18, 15, 21], write an arithmetic expression that equals 18.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 18 |
[
"((23 + 17) + 22)",
"(17 + (23 + 22))",
"(23 + (17 + 22))",
"(((1 * 23) + 17) + 22)",
"(((23 / 1) + 17) + 22)",
"((23 + (1 * 17)) + 22)",
"((23 + (17 / 1)) + 22)",
"((1 * (23 + 17)) + 22)",
"(((23 + 17) / 1) + 22)",
"((23 + 17) + (1 * 22))",
"((23 + 17) + (22 / 1))",
"((1 * 17) + (23 + 22))",
... | ((22 + 17) + 23) | bucket_a | ((22 + 17) + 23) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.332205 | 21,001 | {
"canonical_solution": "((22 + 17) + 23)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"r... | 4 | 28 | [
1,
25
] | [
1,
23,
17,
22
] | {
"completion_tokens": 1777,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"wrong_value": 5
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00528 | Using the numbers [1, 23, 17, 22], write an arithmetic expression that equals 62.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 62 |
[
"((6 + (2 * 19)) + 9)",
"((2 * 19) + (6 + 9))",
"(((6 + 2) * 9) - 19)",
"(6 + ((2 * 19) + 9))"
] | ((9 + 6) + (19 * 2)) | bucket_a | ((9 + 6) + (19 * 2)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.386294 | 21,001 | {
"canonical_solution": "((9 + 6) + (19 * 2))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 4 | [
1,
25
] | [
6,
2,
19,
9
] | {
"completion_tokens": 6868,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"parse_error": 2,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00540 | Using the numbers [6, 2, 19, 9], write an arithmetic expression that equals 53.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 53 |
[
"(17 - 6)",
"(9 + (6 / 3))",
"((17 - 9) + 3)",
"(17 - (9 - 3))",
"((17 + 3) - 9)",
"((17 - (9 - 6)) - 3)",
"(((6 + 17) - 9) - 3)",
"((6 + (17 - 9)) - 3)",
"((17 - 9) + (6 - 3))",
"((6 + 17) - (9 + 3))",
"(17 - ((9 - 6) + 3))",
"(17 - (9 - (6 - 3)))",
"(17 - ((9 + 3) - 6))",
"((17 - 3) - (9... | (3 + (17 - 9)) | bucket_a | (3 + (17 - 9)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.044522 | 21,001 | {
"canonical_solution": "(3 + (17 - 9))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 21 | [
1,
25
] | [
6,
9,
17,
3
] | {
"completion_tokens": 2758,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_positive_intermediate": 2,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00564 | Using the numbers [6, 9, 17, 3], write an arithmetic expression that equals 11.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 11 |
[
"(((21 + 18) + 3) + 20)",
"((18 + (21 + 3)) + 20)",
"((21 + (18 + 3)) + 20)",
"((18 + 3) + (21 + 20))",
"((21 + 3) + (18 + 20))",
"(3 + ((21 + 18) + 20))",
"(3 + (18 + (21 + 20)))",
"(3 + (21 + (18 + 20)))",
"((21 + 18) + (3 + 20))",
"(18 + ((21 + 3) + 20))",
"(18 + (3 + (21 + 20)))",
"(18 + (... | ((20 + 3) + (18 + 21)) | bucket_a | ((20 + 3) + (18 + 21)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((20 + 3) + (18 + 21))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
21,
18,
3,
20
] | {
"completion_tokens": 3602,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 1,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00600 | Using the numbers [21, 18, 3, 20], write an arithmetic expression that equals 62.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 62 |
[
"(6 * 8)",
"(6 + (3 * 14))",
"(3 * ((8 - 6) + 14))",
"(3 * (8 + (14 - 6)))",
"(3 * ((8 + 14) - 6))"
] | (6 * 8) | bucket_a | (6 * 8) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.609438 | 21,001 | {
"canonical_solution": "(6 * 8)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_a... | 4 | 5 | [
1,
25
] | [
6,
3,
8,
14
] | {
"completion_tokens": 3397,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"parse_error": 1,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00614 | Using the numbers [6, 3, 8, 14], write an arithmetic expression that equals 48.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 48 |
[
"(((17 + 18) + 21) + 3)",
"((18 + (17 + 21)) + 3)",
"((17 + (18 + 21)) + 3)",
"((18 + 21) + (17 + 3))",
"((17 + 21) + (18 + 3))",
"(21 + ((17 + 18) + 3))",
"(21 + (18 + (17 + 3)))",
"(21 + (17 + (18 + 3)))",
"((17 + 18) + (21 + 3))",
"(18 + ((17 + 21) + 3))",
"(18 + (21 + (17 + 3)))",
"(18 + (... | ((3 + (18 + 21)) + 17) | bucket_a | ((3 + (18 + 21)) + 17) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((3 + (18 + 21)) + 17)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
17,
18,
21,
3
] | {
"completion_tokens": 2924,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 2,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00615 | Using the numbers [17, 18, 21, 3], write an arithmetic expression that equals 59.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 59 |
[
"((7 * 9) + 13)",
"((7 * 13) - (6 + 9))",
"((6 * 13) - (9 - 7))",
"(((7 * 13) - 6) - 9)",
"((7 + (6 * 13)) - 9)",
"(((7 * 13) - 9) - 6)",
"(7 + ((6 * 13) - 9))"
] | (13 + (7 * 9)) | bucket_a | (13 + (7 * 9)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.94591 | 21,001 | {
"canonical_solution": "(13 + (7 * 9))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 7 | [
1,
25
] | [
7,
6,
9,
13
] | {
"completion_tokens": 5527,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 1,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00619 | Using the numbers [7, 6, 9, 13], write an arithmetic expression that equals 76.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 76 |
[
"(19 - 5)",
"((19 * 1) - 5)",
"((19 / 1) - 5)",
"(1 * (19 - 5))",
"((19 - 5) / 1)",
"(19 - (1 * 5))",
"(19 - (5 / 1))",
"((19 + 5) - 10)",
"(5 + (19 - 10))",
"(19 - (10 - 5))",
"((5 - 1) + 10)",
"(5 + (10 - 1))",
"((5 + 10) - 1)",
"(((19 + 1) / 5) + 10)",
"(((19 * 1) + 5) - 10)",
"(((1... | (19 - 5) | bucket_a | (19 - 5) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.637586 | 21,001 | {
"canonical_solution": "(19 - 5)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 38 | [
1,
25
] | [
19,
1,
5,
10
] | {
"completion_tokens": 2313,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_positive_intermediate": 2,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00629 | Using the numbers [19, 1, 5, 10], write an arithmetic expression that equals 14.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 14 |
[
"((20 - 2) + 10)",
"((20 + 10) - 2)",
"(20 + (10 - 2))",
"(20 + (2 * 4))",
"(2 * (10 + 4))",
"(((20 + 2) + 10) - 4)",
"((2 + (20 + 10)) - 4)",
"((20 + (2 + 10)) - 4)",
"((2 + 10) + (20 - 4))",
"((20 + 10) - (4 - 2))",
"((20 + 10) - (4 / 2))",
"(10 + ((20 + 2) - 4))",
"(10 + (2 + (20 - 4)))",... | (2 * (4 + 10)) | bucket_a | (2 * (4 + 10)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.295837 | 21,001 | {
"canonical_solution": "(2 * (4 + 10))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 27 | [
1,
25
] | [
20,
2,
10,
4
] | {
"completion_tokens": 3995,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 3,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00639 | Using the numbers [20, 2, 10, 4], write an arithmetic expression that equals 28.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 28 |
[
"(6 * 12)",
"(12 * 6)"
] | (6 * 12) | bucket_a | (6 * 12) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -0.693147 | 21,001 | {
"canonical_solution": "(6 * 12)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 2 | [
1,
25
] | [
6,
12,
19,
6
] | {
"completion_tokens": 5002,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"no_box": 1,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00649 | Using the numbers [6, 12, 19, 6], write an arithmetic expression that equals 72.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 72 |
[
"(12 + 18)",
"(((12 + 7) + 18) - 7)",
"((7 + (12 + 18)) - 7)",
"((12 + (7 + 18)) - 7)",
"(((12 - 7) + 18) + 7)",
"(((12 + 18) - 7) + 7)",
"((12 + (18 - 7)) + 7)",
"((7 * (12 + 18)) / 7)",
"((7 + 18) + (12 - 7))",
"((18 - 7) + (12 + 7))",
"((12 + 18) * (7 / 7))",
"((12 + 18) / (7 / 7))",
"(18... | (((12 + 18) - 7) + 7) | bucket_a | (((12 + 18) - 7) + 7) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.258097 | 21,001 | {
"canonical_solution": "(((12 + 18) - 7) + 7)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 26 | [
1,
25
] | [
12,
7,
18,
7
] | {
"completion_tokens": 2508,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 1,
"non_positive_intermediate": 1,
"parse_error": 2,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00657 | Using the numbers [12, 7, 18, 7], write an arithmetic expression that equals 30.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 30 |
[
"(20 - (10 / 5))",
"(20 - (17 - (5 + 10)))",
"(20 - ((17 - 5) - 10))",
"(20 - ((17 - 10) - 5))",
"((5 + 20) - (17 - 10))",
"((10 + 20) - (17 - 5))",
"(((5 + 10) + 20) - 17)",
"((10 + (5 + 20)) - 17)",
"((5 + (10 + 20)) - 17)",
"((5 + 10) + (20 - 17))",
"(10 + (20 - (17 - 5)))",
"(10 + ((5 + 20... | ((5 + (10 + 20)) - 17) | bucket_a | ((5 + (10 + 20)) - 17) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.772589 | 21,001 | {
"canonical_solution": "((5 + (10 + 20)) - 17)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 16 | [
1,
25
] | [
5,
10,
17,
20
] | {
"completion_tokens": 2002,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 2,
"non_positive_intermediate": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00666 | Using the numbers [5, 10, 17, 20], write an arithmetic expression that equals 18.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 18 |
[
"((11 + 21) * 3)",
"(21 + (25 * 3))"
] | ((21 + 11) * 3) | bucket_a | ((21 + 11) * 3) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -0.693147 | 21,001 | {
"canonical_solution": "((21 + 11) * 3)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"re... | 4 | 2 | [
1,
25
] | [
11,
21,
25,
3
] | {
"completion_tokens": 5439,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"no_box": 1,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00668 | Using the numbers [11, 21, 25, 3], write an arithmetic expression that equals 96.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 96 |
[
"(17 * 3)",
"((9 * 17) / 3)",
"(17 * (9 / 3))",
"(((9 + 17) + 3) + 22)",
"((17 + (9 + 3)) + 22)",
"((9 + (17 + 3)) + 22)",
"((17 + 3) + (9 + 22))",
"((9 + 3) + (17 + 22))",
"(3 + ((9 + 17) + 22))",
"(3 + (17 + (9 + 22)))",
"(3 + (9 + (17 + 22)))",
"((9 + 17) + (3 + 22))",
"(17 + ((9 + 3) + 2... | (17 * 3) | bucket_a | (17 * 3) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.890372 | 21,001 | {
"canonical_solution": "(17 * 3)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 18 | [
1,
25
] | [
9,
17,
3,
22
] | {
"completion_tokens": 3928,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_integer_intermediate": 1,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00682 | Using the numbers [9, 17, 3, 22], write an arithmetic expression that equals 51.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 51 |
[
"((17 - 1) + 22)",
"((17 + 22) - 1)",
"(17 + (22 - 1))"
] | (22 + (17 - 1)) | bucket_a | (22 + (17 - 1)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.098612 | 21,001 | {
"canonical_solution": "(22 + (17 - 1))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"re... | 4 | 3 | [
1,
25
] | [
14,
17,
1,
22
] | {
"completion_tokens": 2631,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 2,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00689 | Using the numbers [14, 17, 1, 22], write an arithmetic expression that equals 38.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 38 |
[
"(((21 + 22) + 24) + 7)",
"((22 + (21 + 24)) + 7)",
"((21 + (22 + 24)) + 7)",
"((22 + 24) + (21 + 7))",
"((21 + 24) + (22 + 7))",
"(24 + ((21 + 22) + 7))",
"(24 + (22 + (21 + 7)))",
"(24 + (21 + (22 + 7)))",
"((21 + 22) + (24 + 7))",
"(22 + ((21 + 24) + 7))",
"(22 + (24 + (21 + 7)))",
"(22 + (... | (7 + (24 + (21 + 22))) | bucket_a | (7 + (24 + (21 + 22))) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "(7 + (24 + (21 + 22)))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
21,
22,
24,
7
] | {
"completion_tokens": 2284,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 1,
"parse_error": 3,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00693 | Using the numbers [21, 22, 24, 7], write an arithmetic expression that equals 74.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 74 |
[
"(7 * 2)",
"((19 - 7) + 2)",
"((19 + 2) - 7)",
"(19 - (7 - 2))",
"((7 * 2) * 1)",
"((7 * 2) / 1)",
"(2 * (7 * 1))",
"(2 * (7 / 1))",
"(7 * (2 * 1))",
"(7 * (2 / 1))",
"(((19 + 7) / 2) + 1)",
"(((19 - 7) + 2) * 1)",
"(((19 - 7) + 2) / 1)",
"(((19 + 2) - 7) * 1)",
"(((19 + 2) - 7) / 1)",
... | (2 * (7 / 1)) | bucket_a | (2 * (7 / 1)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.555348 | 21,001 | {
"canonical_solution": "(2 * (7 / 1))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"requ... | 4 | 35 | [
1,
25
] | [
19,
7,
2,
1
] | {
"completion_tokens": 3504,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"invalid_operands": 1,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_00694 | Using the numbers [19, 7, 2, 1], write an arithmetic expression that equals 14.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 14 |
[
"(((25 + 19) + 10) + 7)",
"((19 + (25 + 10)) + 7)",
"((25 + (19 + 10)) + 7)",
"((19 + 10) + (25 + 7))",
"((25 + 10) + (19 + 7))",
"(10 + ((25 + 19) + 7))",
"(10 + (19 + (25 + 7)))",
"(10 + (25 + (19 + 7)))",
"((25 + 19) + (10 + 7))",
"(19 + ((25 + 10) + 7))",
"(19 + (10 + (25 + 7)))",
"(19 + (... | (((25 + 7) + 19) + 10) | bucket_a | (((25 + 7) + 19) + 10) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "(((25 + 7) + 19) + 10)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
25,
19,
10,
7
] | {
"completion_tokens": 2667,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 2,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00700 | Using the numbers [25, 19, 10, 7], write an arithmetic expression that equals 61.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 61 |
[
"(10 + 4)",
"(7 + 7)",
"(((10 + 7) + 4) - 7)",
"((7 + (10 + 4)) - 7)",
"((10 + (7 + 4)) - 7)",
"(((10 - 7) + 4) + 7)",
"(((10 + 4) - 7) + 7)",
"((10 - (7 - 4)) + 7)",
"((7 * (10 + 4)) / 7)",
"(((10 + 4) / 7) * 7)",
"((7 + 4) + (10 - 7))",
"((10 + 7) - (7 - 4))",
"((10 + 4) * (7 / 7))",
"((... | ((10 - (7 - 4)) + 7) | bucket_a | ((10 - (7 - 4)) + 7) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.295837 | 21,001 | {
"canonical_solution": "((10 - (7 - 4)) + 7)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 27 | [
1,
25
] | [
10,
7,
4,
7
] | {
"completion_tokens": 2322,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"non_positive_intermediate": 2,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00707 | Using the numbers [10, 7, 4, 7], write an arithmetic expression that equals 14.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 14 |
[
"(7 + 12)",
"((20 - 7) + 6)",
"(20 - (7 - 6))",
"((20 + 6) - 7)",
"(((12 - 7) + 20) - 6)",
"((12 + (20 - 7)) - 6)",
"(((12 + 20) - 7) - 6)",
"((12 + 20) - (7 + 6))",
"((20 - 7) + (12 - 6))",
"(20 - (6 - (12 - 7)))",
"(20 - ((7 + 6) - 12))",
"(20 - (7 - (12 - 6)))",
"((12 - 7) + (20 - 6))",
... | (12 + 7) | bucket_a | (12 + 7) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.944439 | 21,001 | {
"canonical_solution": "(12 + 7)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 19 | [
1,
25
] | [
7,
12,
20,
6
] | {
"completion_tokens": 2777,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"non_positive_intermediate": 1,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00712 | Using the numbers [7, 12, 20, 6], write an arithmetic expression that equals 19.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 19 |
[
"(((13 - 8) + 13) + 21)",
"(((13 + 13) - 8) + 21)",
"((13 + (13 - 8)) + 21)",
"((13 - 8) + (13 + 21))",
"((13 + 13) + (21 - 8))",
"(13 + ((13 - 8) + 21))",
"(13 + ((13 + 21) - 8))",
"(13 + (13 + (21 - 8)))",
"(((13 + 13) + 21) - 8)",
"((13 + (13 + 21)) - 8)"
] | (((13 + 21) - 8) + 13) | bucket_a | (((13 + 21) - 8) + 13) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.302585 | 21,001 | {
"canonical_solution": "(((13 + 21) - 8) + 13)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 10 | [
1,
25
] | [
13,
8,
13,
21
] | {
"completion_tokens": 3616,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 3,
"non_positive_intermediate": 1,
"parse_error": 1,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00736 | Using the numbers [13, 8, 13, 21], write an arithmetic expression that equals 39.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 39 |
[
"(((23 + 15) + 25) + 16)",
"((15 + (23 + 25)) + 16)",
"((23 + (15 + 25)) + 16)",
"((15 + 25) + (23 + 16))",
"((23 + 25) + (15 + 16))",
"(25 + ((23 + 15) + 16))",
"(25 + (15 + (23 + 16)))",
"(25 + (23 + (15 + 16)))",
"((23 + 15) + (25 + 16))",
"(15 + ((23 + 25) + 16))",
"(15 + (25 + (23 + 16)))",... | (16 + ((25 + 23) + 15)) | bucket_a | (16 + ((25 + 23) + 15)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "(16 + ((25 + 23) + 15))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,... | 4 | 15 | [
1,
25
] | [
23,
15,
25,
16
] | {
"completion_tokens": 3205,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"invalid_operands": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_00751 | Using the numbers [23, 15, 25, 16], write an arithmetic expression that equals 79.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as a... | train | easy | 79 |
[
"(11 + 24)",
"((22 - 11) + 24)",
"((22 + 24) - 11)",
"(22 + (24 - 11))",
"(((22 / 22) * 11) + 24)",
"((11 / (22 / 22)) + 24)",
"(((22 + 11) - 22) + 24)",
"(((22 * 11) / 22) + 24)",
"((22 - (22 - 11)) + 24)",
"((22 / (22 / 11)) + 24)",
"((22 + 11) + (24 - 22))",
"((22 + 24) - (22 - 11))",
"(1... | (11 + 24) | bucket_a | (11 + 24) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.258097 | 21,001 | {
"canonical_solution": "(11 + 24)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required... | 4 | 26 | [
1,
25
] | [
22,
22,
11,
24
] | {
"completion_tokens": 1938,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"non_positive_intermediate": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_00753 | Using the numbers [22, 22, 11, 24], write an arithmetic expression that equals 35.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as a... | train | easy | 35 |
[
"((9 - 8) + (8 * 12))",
"((9 + (8 * 12)) - 8)",
"(9 + ((8 * 12) - 8))"
] | ((8 * 12) + (9 - 8)) | bucket_a | ((8 * 12) + (9 - 8)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.098612 | 21,001 | {
"canonical_solution": "((8 * 12) + (9 - 8))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 3 | [
1,
25
] | [
9,
8,
8,
12
] | {
"completion_tokens": 4431,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"no_box": 1,
"parse_error": 1,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00760 | Using the numbers [9, 8, 8, 12], write an arithmetic expression that equals 97.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 97 |
[
"(((15 + 5) + 15) - 4)",
"((5 + (15 + 15)) - 4)",
"((15 + (5 + 15)) - 4)",
"((5 + 15) + (15 - 4))",
"((15 + 15) + (5 - 4))",
"(15 + ((15 + 5) - 4))",
"(15 + (5 + (15 - 4)))",
"(15 + (15 + (5 - 4)))",
"((15 + 5) + (15 - 4))",
"(5 + ((15 + 15) - 4))",
"(5 + (15 + (15 - 4)))",
"(15 + ((5 + 15) - ... | (((5 - 4) + 15) + 15) | bucket_a | (((5 - 4) + 15) + 15) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.484907 | 21,001 | {
"canonical_solution": "(((5 - 4) + 15) + 15)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 12 | [
1,
25
] | [
15,
5,
15,
4
] | {
"completion_tokens": 3564,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 2,
"parse_error": 3,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00762 | Using the numbers [15, 5, 15, 4], write an arithmetic expression that equals 31.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 31 |
[
"(((21 + 8) + 2) + 22)",
"((8 + (21 + 2)) + 22)",
"((21 + (8 + 2)) + 22)",
"((8 + 2) + (21 + 22))",
"((21 + 2) + (8 + 22))",
"(2 + ((21 + 8) + 22))",
"(2 + (8 + (21 + 22)))",
"(2 + (21 + (8 + 22)))",
"((21 + 8) + (2 + 22))",
"(8 + ((21 + 2) + 22))",
"(8 + (2 + (21 + 22)))",
"(8 + (21 + (2 + 22... | (22 + ((2 + 21) + 8)) | bucket_a | (22 + ((2 + 21) + 8)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "(22 + ((2 + 21) + 8))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
21,
8,
2,
22
] | {
"completion_tokens": 3045,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"wrong_value": 6
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00764 | Using the numbers [21, 8, 2, 22], write an arithmetic expression that equals 53.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 53 |
[
"(25 - (10 - 3))",
"(3 + (25 - 10))",
"((3 + 25) - 10)",
"(25 - ((20 - 10) - 3))",
"(25 - (20 - (10 + 3)))",
"(25 - ((20 - 3) - 10))",
"((10 + 25) - (20 - 3))",
"((10 + 3) + (25 - 20))",
"(3 + (25 - (20 - 10)))",
"(3 + ((10 + 25) - 20))",
"(3 + (10 + (25 - 20)))",
"((3 + 25) - (20 - 10))",
"... | ((3 + 25) - (20 - 10)) | bucket_a | ((3 + 25) - (20 - 10)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.890372 | 21,001 | {
"canonical_solution": "((3 + 25) - (20 - 10))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 18 | [
1,
25
] | [
10,
20,
3,
25
] | {
"completion_tokens": 3317,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 1,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_00765 | Using the numbers [10, 20, 3, 25], write an arithmetic expression that equals 18.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 18 |
[
"((5 + 18) - 13)",
"(18 - (13 - 5))",
"(5 + (18 - 13))"
] | ((18 + 5) - 13) | bucket_a | ((18 + 5) - 13) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.098612 | 21,001 | {
"canonical_solution": "((18 + 5) - 13)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"re... | 4 | 3 | [
1,
25
] | [
5,
18,
13,
18
] | {
"completion_tokens": 3494,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_integer_intermediate": 1,
"non_positive_intermediate": 2,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00766 | Using the numbers [5, 18, 13, 18], write an arithmetic expression that equals 10.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 10 |
[
"((5 + 2) * 9)",
"(18 + (5 * 9))",
"(((5 - 2) * 18) + 9)",
"((5 + 2) * (18 - 9))"
] | (18 + (9 * 5)) | bucket_a | (18 + (9 * 5)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.386294 | 21,001 | {
"canonical_solution": "(18 + (9 * 5))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 4 | [
1,
25
] | [
5,
2,
18,
9
] | {
"completion_tokens": 4331,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 2,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00774 | Using the numbers [5, 2, 18, 9], write an arithmetic expression that equals 63.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 63 |
[
"(((18 + 1) + 10) + 20)",
"((1 + (18 + 10)) + 20)",
"((18 + (1 + 10)) + 20)",
"((1 + 10) + (18 + 20))",
"((18 + 10) + (1 + 20))",
"(10 + ((18 + 1) + 20))",
"(10 + (1 + (18 + 20)))",
"(10 + (18 + (1 + 20)))",
"((18 + 1) + (10 + 20))",
"(1 + ((18 + 10) + 20))",
"(1 + (10 + (18 + 20)))",
"(1 + (1... | ((20 + (18 + 10)) + 1) | bucket_a | ((20 + (18 + 10)) + 1) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((20 + (18 + 10)) + 1)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
18,
1,
10,
20
] | {
"completion_tokens": 4073,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"parse_error": 4,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00782 | Using the numbers [18, 1, 10, 20], write an arithmetic expression that equals 49.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 49 |
[
"(((11 - 3) + 17) + 20)",
"((11 + (17 - 3)) + 20)",
"(((11 + 17) - 3) + 20)",
"((11 + 17) + (20 - 3))",
"((17 - 3) + (11 + 20))",
"(17 + ((11 - 3) + 20))",
"(17 + (11 + (20 - 3)))",
"(17 + ((11 + 20) - 3))",
"((11 - 3) + (17 + 20))",
"(11 + ((17 - 3) + 20))",
"(11 + (17 + (20 - 3)))",
"(11 + (... | ((20 + 11) + (17 - 3)) | bucket_a | ((20 + 11) + (17 - 3)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((20 + 11) + (17 - 3))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
3,
11,
17,
20
] | {
"completion_tokens": 3605,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"parse_error": 3,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_00789 | Using the numbers [3, 11, 17, 20], write an arithmetic expression that equals 45.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 45 |
[
"(18 + 13)",
"((22 + 22) - 13)",
"(22 + (22 - 13))",
"(((22 + 18) - 22) + 13)",
"(((22 * 18) / 22) + 13)",
"((22 - (22 - 18)) + 13)",
"((18 * (22 / 22)) + 13)",
"((18 / (22 / 22)) + 13)",
"(((18 + 22) - 22) + 13)",
"(((18 * 22) / 22) + 13)",
"((18 + 22) - (22 - 13))",
"((22 + 13) - (22 - 18))"... | (18 + 13) | bucket_a | (18 + 13) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.332205 | 21,001 | {
"canonical_solution": "(18 + 13)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required... | 4 | 28 | [
1,
25
] | [
22,
18,
22,
13
] | {
"completion_tokens": 1976,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_positive_intermediate": 4,
"parse_error": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00790 | Using the numbers [22, 18, 22, 13], write an arithmetic expression that equals 31.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as a... | train | easy | 31 |
[
"((15 + 16) + 3)",
"(16 + (15 + 3))",
"(15 + (16 + 3))",
"(((15 * 1) + 16) + 3)",
"(((15 / 1) + 16) + 3)",
"((1 * (15 + 16)) + 3)",
"(((15 + 16) / 1) + 3)",
"((15 + (1 * 16)) + 3)",
"((15 + (16 / 1)) + 3)",
"((1 * 16) + (15 + 3))",
"((16 / 1) + (15 + 3))",
"((15 + 16) + (1 * 3))",
"((15 + 16... | (3 + (15 + 16)) | bucket_a | (3 + (15 + 16)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.332205 | 21,001 | {
"canonical_solution": "(3 + (15 + 16))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"re... | 4 | 28 | [
1,
25
] | [
15,
1,
16,
3
] | {
"completion_tokens": 3597,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 3,
"parse_error": 2,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_00805 | Using the numbers [15, 1, 16, 3], write an arithmetic expression that equals 34.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 34 |
End of preview. Expand in Data Studio
Countdown Qwen3-0.6B Pass@10 Buckets
Countdown arithmetic problems filtered by observed local Qwen/Qwen3-0.6B success rate over 10 rollouts per problem.
Each problem asks for an arithmetic expression that reaches a target using each listed source number at most once. The final answer should be inside \boxed{...}. Canonical solutions are provided, but any verifier-valid expression is accepted.
Subsets
| subset | source bucket | count | observed successes out of 10 |
|---|---|---|---|
| easy | bucket_a | 505 | 4-6 |
| medium | bucket_b | 519 | 1-3 |
| hard | bucket_c | 526 | 1 |
Collection Settings
- Model:
Qwen/Qwen3-0.6B - Rollouts per candidate problem: 10
max_tokens: 1024temperature: 1.0top_p: 0.95- Qwen thinking disabled:
chat_template_kwargs.enable_thinking=false
See manifest.json for summary statistics and the exact source paths from the local collection.
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