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The dataset generation failed
Error code: DatasetGenerationError
Exception: TypeError
Message: Couldn't cast array of type
struct<method: string, expr: string, computed: int64, token: int64>
to
{'method': Value('string'), 'expr': Value('string'), 'computed': Value('int64')}
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1816, in _prepare_split_single
for key, table in generator:
^^^^^^^^^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 613, in wrapped
for item in generator(*args, **kwargs):
~~~~~~~~~^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 343, in _generate_tables
self._cast_table(pa_table, json_field_paths=json_field_paths),
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 132, in _cast_table
pa_table = table_cast(pa_table, self.info.features.arrow_schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2369, in table_cast
return cast_table_to_schema(table, schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2303, in cast_table_to_schema
cast_array_to_feature(
~~~~~~~~~~~~~~~~~~~~~^
table[name] if name in table_column_names else pa.array([None] * len(table), type=schema.field(name).type),
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
feature,
^^^^^^^^
)
^
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 1852, in wrapper
return pa.chunked_array([func(chunk, *args, **kwargs) for chunk in array.chunks])
~~~~^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2059, in cast_array_to_feature
_c(array.field(name) if name in array_fields else null_array, subfeature)
~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 1854, in wrapper
return func(array, *args, **kwargs)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2149, in cast_array_to_feature
raise TypeError(f"Couldn't cast array of type\n{_short_str(array.type)}\nto\n{_short_str(feature)}")
TypeError: Couldn't cast array of type
struct<method: string, expr: string, computed: int64, token: int64>
to
{'method': Value('string'), 'expr': Value('string'), 'computed': Value('int64')}
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1369, in compute_config_parquet_and_info_response
parquet_operations, partial, estimated_dataset_info = stream_convert_to_parquet(
~~~~~~~~~~~~~~~~~~~~~~~~~^
builder, max_dataset_size_bytes=max_dataset_size_bytes
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
)
^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 948, in stream_convert_to_parquet
builder._prepare_split(split_generator=splits_generators[split], file_format="parquet")
~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1683, in _prepare_split
for job_id, done, content in self._prepare_split_single(
~~~~~~~~~~~~~~~~~~~~~~~~~~^
gen_kwargs=gen_kwargs, job_id=job_id, **_prepare_split_args
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
):
^
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1869, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
id string | problem_id string | chapter string | prompt string | response string | answer int64 | created_from string | _arith_check dict | reasoning_quality string |
|---|---|---|---|---|---|---|---|---|
787332b29713a5ad6acf1e333a8aad596e44eb297cecac15cf981bc8a0dcb346 | NN_001-9a4b873a | natural_numbers | Find 1 + 2 + ... + 97. What is its exact value? | Goal: compute value for template NN_001. Givens: n=97 Using expression: (n*(n+1))//2 Substitute values: (97*(97+1))//2 Compute result → 4753. Therefore the final answer is 4753. | 4,753 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "(97*(97+1))//2",
"computed": 4753
},
"found_expr": "(97*(97+1))//2"
} | minimal |
4bc74ed98448fc305998f1d5c3ff58a18c9a49dc73dd828a430ac160b9456107 | NN_005-81516094 | natural_numbers | Find the count of multiples of 12 in the interval [580,8148]. | Goal: compute value for template NN_005. Givens: L=580, R=8148, k=12 Using expression: ((R//k) - ((L-1)//k)) Substitute values: ((8148//12) - ((580-1)//12)) Compute result → 631. Therefore the final answer is 631. | 631 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((8148//12) - ((580-1)//12))",
"computed": 631
},
"found_expr": "((8148//12) - ((580-1)//12))"
} | minimal |
1e88882662520cf25ea4590496158e21e275e04264000553ff0e6dbfe7c08afe | NN_007-d60e6297 | natural_numbers | Between 1 and 10, inclusive, how many numbers are even? | Goal: compute value for template NN_007. Givens: L=1, R=10 Using expression: ((R//2) - ((L-1)//2)) Substitute values: ((10//2) - ((1-1)//2)) Compute result → 5. Therefore the final answer is 5. | 5 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((10//2) - ((1-1)//2))",
"computed": 5
},
"found_expr": "((10//2) - ((1-1)//2))"
} | minimal |
004081249d631b11f7e70031003f94b02d4007abad0df27164814eb6d314c232 | NN_006-1d0f7ac0 | natural_numbers | What is the last (units) digit of 329? | Problem (NN_006): What is the last (units) digit of 329? Known: num=329 Approach: Digit sum of 329 = 3 + 2 + 9 = 14. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 14 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "3 + 2 + 9",
"computed": 14
},
"found_expr": "3 + 2 + 9"
} | rich |
441a3ed3712848a3f53aeb40ba2004524dbb5cee4e974fd6c9194598f442547a | NN_001-220a2643 | natural_numbers | What is the sum of all natural numbers from 1 to 151 inclusive? | Goal: compute value for template NN_001. Givens: n=151 Using expression: (n*(n+1))//2 Substitute values: (151*(151+1))//2 Compute result → 11476. Therefore the final answer is 11476. | 11,476 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "(151*(151+1))//2",
"computed": 11476
},
"found_expr": "(151*(151+1))//2"
} | minimal |
4db15fef6c85011a876e651b20c18b1b62846a41966b866e6c358387f7cd7efe | NN_001-e201f88f | natural_numbers | What is the sum of all natural numbers from 1 to 22 inclusive? | Goal: compute value for template NN_001. Givens: n=22 Using expression: (n*(n+1))//2 Substitute values: (22*(22+1))//2 Compute result → 253. Therefore the final answer is 253. | 253 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "(22*(22+1))//2",
"computed": 253
},
"found_expr": "(22*(22+1))//2"
} | minimal |
c8b544fa5b2d358a313ce243782a52e40e1af03e41319bcaed07b65c70e3961b | NN_001-1a2219e4 | natural_numbers | What is the sum of all natural numbers from 1 to 36 inclusive? | Goal: compute value for template NN_001. Givens: n=36 Using expression: (n*(n+1))//2 Substitute values: (36*(36+1))//2 Compute result → 666. Therefore the final answer is 666. | 666 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "(36*(36+1))//2",
"computed": 666
},
"found_expr": "(36*(36+1))//2"
} | minimal |
23f55ae8c35e7cbd108ae3502d98182d8e900e6097d37755fd709c90938978a3 | NN_007-3e16e1a8 | natural_numbers | How many even integers are there between 12 and 454 inclusive? | Goal: compute value for template NN_007. Givens: L=12, R=454 Using expression: ((R//2) - ((L-1)//2)) Substitute values: ((454//2) - ((12-1)//2)) Compute result → 222. Therefore the final answer is 222. | 222 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((454//2) - ((12-1)//2))",
"computed": 222
},
"found_expr": "((454//2) - ((12-1)//2))"
} | minimal |
31b7082f3dada2395261b8a22ebfe3657197ad5044171093fc02d3d97cecbda5 | NN_006-c79a0a3a | natural_numbers | What digit appears in the ones place of 29226? | Problem (NN_006): What digit appears in the ones place of 29226? Known: num=29226 Approach: Digit sum of 29226 = 2 + 9 + 2 + 2 + 6 = 21. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 21 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "2 + 9 + 2 + 2 + 6",
"computed": 21
},
"found_expr": "2 + 9 + 2 + 2 + 6"
} | rich |
085e8fc23adbb2a04894826747c9ea2769419f49eadc781a6055a67405c9dadf | NN_002-9e5eefce | natural_numbers | Compute the sum of 24 consecutive natural numbers starting at 128. | Goal: compute value for template NN_002. Givens: a=128, n=24 Using expression: ((n*(2*a + (n-1)*1))//2) Substitute values: ((24*(2*128 + (24-1)*1))//2) Compute result → 3348. Therefore the final answer is 3348. | 3,348 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((24*(2*128 + (24-1)*1))//2)",
"computed": 3348
},
"found_expr": "((24*(2*128 + (24-1)*1))//2)"
} | minimal |
c60e6a70463a888ffcd2a3755c6fdac0c86379414d990ca5c2c3db96d790b0a1 | NN_008-00dff991 | natural_numbers | What is the multiplication of the digits of 343? | Problem (NN_008): What is the multiplication of the digits of 343? Step 1: Known: num=343 Step 2: Approach: Digit sum of 343 = 3 + 4 + 3 = 10. Step 3: Compute and conclude. | 10 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "3 + 4 + 3",
"computed": 10
},
"found_expr": "3 + 4 + 3"
} | rich |
1371aac399b53603664f28d5af8554662cc70285c07fc8c2c33240c50ba2d893 | NN_012-78b59192 | natural_numbers | What is the digit-range (max minus min digit) of 16647? | Problem (NN_012): What is the digit-range (max minus min digit) of 16647? Known: num=16647 Approach: Digit sum of 16647 = 1 + 6 + 6 + 4 + 7 = 24. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 24 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "1 + 6 + 6 + 4 + 7",
"computed": 24
},
"found_expr": "1 + 6 + 6 + 4 + 7"
} | rich |
8171dae6262d491eb77adb82a53db59530ae9c1d2666d2613d457b6e2ab2b5cc | NN_008-1c446f03 | natural_numbers | Find the product of all digits in 178. | Problem (NN_008): Find the product of all digits in 178. Step 1: Known: num=178 Step 2: Approach: Digit sum of 178 = 1 + 7 + 8 = 16. Step 3: Compute and conclude. | 16 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "1 + 7 + 8",
"computed": 16
},
"found_expr": "1 + 7 + 8"
} | rich |
cc1f65aeea4f64c45f9b6e05385e05990f37776eb44f8e7a041aecff0ad07a2b | NN_003-78dd17ca | natural_numbers | Compute the digit-sum of 176. | Problem (NN_003): Compute the digit-sum of 176. Known: num=176 Approach: Digit sum of 176 = 1 + 7 + 6 = 14. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 14 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "1 + 7 + 6",
"computed": 14
},
"found_expr": "1 + 7 + 6"
} | rich |
58c075f993be0be43a6fbe3030663f7c65a1c0155ba5372ac0daacf7de7bc146 | NN_002-b1b8bd29 | natural_numbers | Compute the sum of 7 consecutive natural numbers starting at 9. | Goal: compute value for template NN_002. Givens: a=9, n=7 Using expression: ((n*(2*a + (n-1)*1))//2) Substitute values: ((7*(2*9 + (7-1)*1))//2) Compute result → 84. Therefore the final answer is 84. | 84 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((7*(2*9 + (7-1)*1))//2)",
"computed": 84
},
"found_expr": "((7*(2*9 + (7-1)*1))//2)"
} | minimal |
ce7869429be0792b371ae3a5ac51e36d3300df84082d5cad2d97d186e44d4ef8 | NN_011-ffa1fa3f | natural_numbers | How many trailing zeros are there in 20! (factorial)? | Problem (NN_011): How many trailing zeros are there in 20! (factorial)? Step 1: Known: n=20 Step 2: Approach: Digit sum of 20 = 2 + 0 = 2. Step 3: Compute and conclude. | 2 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "2 + 0",
"computed": 2
},
"found_expr": "2 + 0"
} | rich |
822ba45053d0af5582a0f0a68ccf8a6be7d65b93f9e262dc655dbf82dc42be21 | NN_002-ea7cb66e | natural_numbers | Compute the sum of 82 consecutive natural numbers starting at 472. | Goal: compute value for template NN_002. Givens: a=472, n=82 Using expression: ((n*(2*a + (n-1)*1))//2) Substitute values: ((82*(2*472 + (82-1)*1))//2) Compute result → 42025. Therefore the final answer is 42025. | 42,025 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((82*(2*472 + (82-1)*1))//2)",
"computed": 42025
},
"found_expr": "((82*(2*472 + (82-1)*1))//2)"
} | minimal |
33564d2d39b0b0466758b6135fb572fdcc0fa1219c9d302b68a8cb05d9754b4d | NN_006-e9ed51fd | natural_numbers | Find the units place digit of the number 180. | Problem (NN_006): Find the units place digit of the number 180. Known: num=180 Approach: Digit sum of 180 = 1 + 8 + 0 = 9. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 9 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "1 + 8 + 0",
"computed": 9
},
"found_expr": "1 + 8 + 0"
} | rich |
f34c7a53a85f58a3a827fa58123912604ef1d5b42025bc526ea5cb0e4ac0ec02 | NN_012-850b3f03 | natural_numbers | What is the digit-range (max minus min digit) of 18698? | Problem (NN_012): What is the digit-range (max minus min digit) of 18698? Known: num=18698 Approach: Digit sum of 18698 = 1 + 8 + 6 + 9 + 8 = 32. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 32 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "1 + 8 + 6 + 9 + 8",
"computed": 32
},
"found_expr": "1 + 8 + 6 + 9 + 8"
} | rich |
340d370562de40169a0da0a03ebbd6b5fe2fa0680155362c3dbeaf6a564240bd | NN_006-5504ac90 | natural_numbers | Find the units place digit of the number 695448. | Problem (NN_006): Find the units place digit of the number 695448. Known: num=695448 Approach: Digit sum of 695448 = 6 + 9 + 5 + 4 + 4 + 8 = 36. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 36 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "6 + 9 + 5 + 4 + 4 + 8",
"computed": 36
},
"found_expr": "6 + 9 + 5 + 4 + 4 + 8"
} | rich |
a5f8884ec4986b4d4da5f7d36d6fc0aca67e7f9864b41b31ece903cdb231891c | NN_009-a82f4dbb | natural_numbers | From the first 4 natural numbers, how many unordered pairs can be selected? | Goal: compute value for template NN_009. Givens: n=4 Using expression: (n*(n-1))//2 Substitute values: (4*(4-1))//2 Compute result → 6. Therefore the final answer is 6. | 6 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "(4*(4-1))//2",
"computed": 6
},
"found_expr": "(4*(4-1))//2"
} | minimal |
95230f9bade4c34af4538a8ff8a9f2dbd205d2789ca4bbcf4d1d7610896958a3 | NN_001-2cd4f363 | natural_numbers | What is the sum of all natural numbers from 1 to 114 inclusive? | Goal: compute value for template NN_001. Givens: n=114 Using expression: (n*(n+1))//2 Substitute values: (114*(114+1))//2 Compute result → 6555. Therefore the final answer is 6555. | 6,555 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "(114*(114+1))//2",
"computed": 6555
},
"found_expr": "(114*(114+1))//2"
} | minimal |
cc5c0bb6bcc952f3982b67627275818754a2ce15547637f8984c0fd14ea05e35 | NN_002-88d848e5 | natural_numbers | Compute the sum of 29 consecutive natural numbers starting at 166. | Goal: compute value for template NN_002. Givens: a=166, n=29 Using expression: ((n*(2*a + (n-1)*1))//2) Substitute values: ((29*(2*166 + (29-1)*1))//2) Compute result → 5220. Therefore the final answer is 5220. | 5,220 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((29*(2*166 + (29-1)*1))//2)",
"computed": 5220
},
"found_expr": "((29*(2*166 + (29-1)*1))//2)"
} | minimal |
1f6c0091a044096be4f3b74dd35dc41c1eb68c3e4f2ce4849bbfda7c7f5b42b9 | NN_012-feeab5db | natural_numbers | Find the difference between the largest and smallest digit of 660. | Problem (NN_012): Find the difference between the largest and smallest digit of 660. Known: num=660 Approach: Digit sum of 660 = 6 + 6 + 0 = 12. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 12 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "6 + 6 + 0",
"computed": 12
},
"found_expr": "6 + 6 + 0"
} | rich |
cd7ef383931e1b5ea7a3b8e14dad1d20a63f2166290cd1b3c0db21750acfc15d | NN_008-77e78258 | natural_numbers | Find the product of all digits in 712. | Problem (NN_008): Find the product of all digits in 712. Step 1: Known: num=712 Step 2: Approach: Digit sum of 712 = 7 + 1 + 2 = 10. Step 3: Compute and conclude. | 10 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "7 + 1 + 2",
"computed": 10
},
"found_expr": "7 + 1 + 2"
} | rich |
7c2181f781fedaa15917b3f97c0884346d17400e52f157a0708c236742b11860 | NN_008-972a921a | natural_numbers | Find the product of all digits in 4430. | Problem (NN_008): Find the product of all digits in 4430. Step 1: Known: num=4430 Step 2: Approach: Digit sum of 4430 = 4 + 4 + 3 + 0 = 11. Step 3: Compute and conclude. | 11 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "4 + 4 + 3 + 0",
"computed": 11
},
"found_expr": "4 + 4 + 3 + 0"
} | rich |
887bec5f9b57a4e6d95a5101e1fb73ba8a753ccb885a7814aaec9e9399acf2d7 | NN_008-33acffa6 | natural_numbers | Find the product of all digits in 925. | Problem (NN_008): Find the product of all digits in 925. Step 1: Known: num=925 Step 2: Approach: Digit sum of 925 = 9 + 2 + 5 = 16. Step 3: Compute and conclude. | 16 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "9 + 2 + 5",
"computed": 16
},
"found_expr": "9 + 2 + 5"
} | rich |
de27223b6d808458167a87ab0a085949341f8b7207ebb63f3599780af25c9427 | NN_005-cf441e6c | natural_numbers | Between 6 and 35, how many numbers are multiples of 2? | Goal: compute value for template NN_005. Givens: L=6, R=35, k=2 Using expression: ((R//k) - ((L-1)//k)) Substitute values: ((35//2) - ((6-1)//2)) Compute result → 15. Therefore the final answer is 15. | 15 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((35//2) - ((6-1)//2))",
"computed": 15
},
"found_expr": "((35//2) - ((6-1)//2))"
} | minimal |
34dfaa5dfb525355ed660e09265dfa61feffb2cd277e4d00ca49852569b310ef | NN_001-57697313 | natural_numbers | Compute the sum of the first 128 natural numbers. | Goal: compute value for template NN_001. Givens: n=128 Using expression: (n*(n+1))//2 Substitute values: (128*(128+1))//2 Compute result → 8256. Therefore the final answer is 8256. | 8,256 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "(128*(128+1))//2",
"computed": 8256
},
"found_expr": "(128*(128+1))//2"
} | minimal |
4d0e7c7ce7701f91363c4ae95580e328dcf148392b47451a46f3be8f0c857ec6 | NN_003-c7b29f02 | natural_numbers | Compute the digit-sum of 847. | Problem (NN_003): Compute the digit-sum of 847. Known: num=847 Approach: Digit sum of 847 = 8 + 4 + 7 = 19. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 19 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "8 + 4 + 7",
"computed": 19
},
"found_expr": "8 + 4 + 7"
} | rich |
abfc6fa6e4aa55609ee8079f8d2f28bf7909cdab67f61f94206a42dc86892640 | NN_007-682179ed | natural_numbers | How many even integers are there between 1 and 8 inclusive? | Goal: compute value for template NN_007. Givens: L=1, R=8 Using expression: ((R//2) - ((L-1)//2)) Substitute values: ((8//2) - ((1-1)//2)) Compute result → 4. Therefore the final answer is 4. | 4 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((8//2) - ((1-1)//2))",
"computed": 4
},
"found_expr": "((8//2) - ((1-1)//2))"
} | minimal |
6b41d238cd53b1a4a96c3435895cbf12cc0ae66eb2850d85af678d168eec60fb | NN_001-f79f4f4b | natural_numbers | Compute the sum of the first 82 natural numbers. | Goal: compute value for template NN_001. Givens: n=82 Using expression: (n*(n+1))//2 Substitute values: (82*(82+1))//2 Compute result → 3403. Therefore the final answer is 3403. | 3,403 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "(82*(82+1))//2",
"computed": 3403
},
"found_expr": "(82*(82+1))//2"
} | minimal |
e1886e7caab6d6969205d1e3b76a2721a61b86e83ff60a1111ba5d40bf8a6d20 | NN_003-13329df3 | natural_numbers | Compute the digit-sum of 60962. | Problem (NN_003): Compute the digit-sum of 60962. Known: num=60962 Approach: Digit sum of 60962 = 6 + 0 + 9 + 6 + 2 = 23. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 23 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "6 + 0 + 9 + 6 + 2",
"computed": 23
},
"found_expr": "6 + 0 + 9 + 6 + 2"
} | rich |
f2fdc3de4424b3c7133a0e26fbfa317f9ef749fcd832926def2ebba5a11f2c9d | NN_006-d532e731 | natural_numbers | What is the last (units) digit of 87842? | Problem (NN_006): What is the last (units) digit of 87842? Known: num=87842 Approach: Digit sum of 87842 = 8 + 7 + 8 + 4 + 2 = 29. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 29 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "8 + 7 + 8 + 4 + 2",
"computed": 29
},
"found_expr": "8 + 7 + 8 + 4 + 2"
} | rich |
5389a6c0d8444c465eba5a95b58f7df73ed8a5be6f6363fc6df0c2161f34df8b | NN_006-9e1ea74a | natural_numbers | What digit appears in the ones place of 806900? | Problem (NN_006): What digit appears in the ones place of 806900? Known: num=806900 Approach: Digit sum of 806900 = 8 + 0 + 6 + 9 + 0 + 0 = 23. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 23 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "8 + 0 + 6 + 9 + 0 + 0",
"computed": 23
},
"found_expr": "8 + 0 + 6 + 9 + 0 + 0"
} | rich |
247f660f2e99e1a4a2c2c3a95af15f0822e6244937f8063b2d5342c7cc6f0c96 | NN_001-142ecfea | natural_numbers | Find 1 + 2 + ... + 102. What is its exact value? | Goal: compute value for template NN_001. Givens: n=102 Using expression: (n*(n+1))//2 Substitute values: (102*(102+1))//2 Compute result → 5253. Therefore the final answer is 5253. | 5,253 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "(102*(102+1))//2",
"computed": 5253
},
"found_expr": "(102*(102+1))//2"
} | minimal |
72bf3ecba5120200b85e8318c27ccfb12d5c46b95a2486e283bc59285bd49f9b | NN_006-02629e9b | natural_numbers | Find the units place digit of the number 42054. | Problem (NN_006): Find the units place digit of the number 42054. Known: num=42054 Approach: Digit sum of 42054 = 4 + 2 + 0 + 5 + 4 = 15. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 15 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "4 + 2 + 0 + 5 + 4",
"computed": 15
},
"found_expr": "4 + 2 + 0 + 5 + 4"
} | rich |
b26b0e20ffc445ea5bbadee0f9acf3956cfbe6da5238344c0129aaac44c6d5d6 | NN_003-47e51fd3 | natural_numbers | Find the sum of all decimal digits in 498162. | Problem (NN_003): Find the sum of all decimal digits in 498162. Known: num=498162 Approach: Digit sum of 498162 = 4 + 9 + 8 + 1 + 6 + 2 = 30. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 30 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "4 + 9 + 8 + 1 + 6 + 2",
"computed": 30
},
"found_expr": "4 + 9 + 8 + 1 + 6 + 2"
} | rich |
d8cb01a86e1128293d14bdb88168b18a289bd99ee3c0125dc9266c8cb5d32030 | NN_011-0780f2d5 | natural_numbers | How many trailing zeros are there in 19! (factorial)? | Problem (NN_011): How many trailing zeros are there in 19! (factorial)? Step 1: Known: n=19 Step 2: Approach: Digit sum of 19 = 1 + 9 = 10. Step 3: Compute and conclude. | 10 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "1 + 9",
"computed": 10
},
"found_expr": "1 + 9"
} | rich |
f871ac69c78f30ebba969b3136baa7a084a1fc20e87ea897e97bdc1ae7919327 | NN_002-bd2fa56c | natural_numbers | Compute the sum of 22 consecutive natural numbers starting at 22. | Goal: compute value for template NN_002. Givens: a=22, n=22 Using expression: ((n*(2*a + (n-1)*1))//2) Substitute values: ((22*(2*22 + (22-1)*1))//2) Compute result → 715. Therefore the final answer is 715. | 715 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((22*(2*22 + (22-1)*1))//2)",
"computed": 715
},
"found_expr": "((22*(2*22 + (22-1)*1))//2)"
} | minimal |
8c1fe1f48cb30d3e34abf79ab6100a2dffbfb946163cf93ee8aeac75fcdb5260 | NN_001-2d28d4ca | natural_numbers | What is the sum of all natural numbers from 1 to 18 inclusive? | Goal: compute value for template NN_001. Givens: n=18 Using expression: (n*(n+1))//2 Substitute values: (18*(18+1))//2 Compute result → 171. Therefore the final answer is 171. | 171 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "(18*(18+1))//2",
"computed": 171
},
"found_expr": "(18*(18+1))//2"
} | minimal |
c8e66ac57c5358c419b93e220e1cf00c9225e38d3874bb464142630305fc55d4 | NN_006-9215cb5e | natural_numbers | Find the units place digit of the number 350434. | Problem (NN_006): Find the units place digit of the number 350434. Known: num=350434 Approach: Digit sum of 350434 = 3 + 5 + 0 + 4 + 3 + 4 = 19. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 19 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "3 + 5 + 0 + 4 + 3 + 4",
"computed": 19
},
"found_expr": "3 + 5 + 0 + 4 + 3 + 4"
} | rich |
2d43f705b68078c827dd03b9530d911a31d1f05de946a06c48c34596f6f78e09 | NN_002-bfcce305 | natural_numbers | Compute the sum of 19 consecutive natural numbers starting at 112. | Goal: compute value for template NN_002. Givens: a=112, n=19 Using expression: ((n*(2*a + (n-1)*1))//2) Substitute values: ((19*(2*112 + (19-1)*1))//2) Compute result → 2299. Therefore the final answer is 2299. | 2,299 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((19*(2*112 + (19-1)*1))//2)",
"computed": 2299
},
"found_expr": "((19*(2*112 + (19-1)*1))//2)"
} | minimal |
9182fb948fc13cf44f5949319ac2d9f868af9147d4080a640fe1349e128e9115 | NN_008-0bbb1cbc | natural_numbers | Find the product of all digits in 5076. | Problem (NN_008): Find the product of all digits in 5076. Step 1: Known: num=5076 Step 2: Approach: Digit sum of 5076 = 5 + 0 + 7 + 6 = 18. Step 3: Compute and conclude. | 18 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "5 + 0 + 7 + 6",
"computed": 18
},
"found_expr": "5 + 0 + 7 + 6"
} | rich |
99922d888d8feec21e4b936ec25556f09b75e8bf352a3350da0e5877e9469a1e | NN_003-060a6ca3 | natural_numbers | Find the sum of all decimal digits in 29569. | Problem (NN_003): Find the sum of all decimal digits in 29569. Known: num=29569 Approach: Digit sum of 29569 = 2 + 9 + 5 + 6 + 9 = 31. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 31 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "2 + 9 + 5 + 6 + 9",
"computed": 31
},
"found_expr": "2 + 9 + 5 + 6 + 9"
} | rich |
4a7fbd2ece6138bae0a2411b1fc7b1e4432179381c8d8cd176c7d1dbf343d3b7 | NN_007-507c9302 | natural_numbers | Between 17 and 343, inclusive, how many numbers are even? | Goal: compute value for template NN_007. Givens: L=17, R=343 Using expression: ((R//2) - ((L-1)//2)) Substitute values: ((343//2) - ((17-1)//2)) Compute result → 163. Therefore the final answer is 163. | 163 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((343//2) - ((17-1)//2))",
"computed": 163
},
"found_expr": "((343//2) - ((17-1)//2))"
} | minimal |
0f989a4b7e99363f3a865550a067fda26d631b42ba7e66f5860f0e3bbf7a6f4c | NN_003-0f106a18 | natural_numbers | What is the sum of digits of the number 83459? | Problem (NN_003): What is the sum of digits of the number 83459? Known: num=83459 Approach: Digit sum of 83459 = 8 + 3 + 4 + 5 + 9 = 29. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 29 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "8 + 3 + 4 + 5 + 9",
"computed": 29
},
"found_expr": "8 + 3 + 4 + 5 + 9"
} | rich |
02af346829a7e64e14de0d21b9a039b2c943e07c4a718c1ab32875a7ec83d132 | NN_012-897c3d05 | natural_numbers | Find the difference between the largest and smallest digit of 37212. | Problem (NN_012): Find the difference between the largest and smallest digit of 37212. Known: num=37212 Approach: Digit sum of 37212 = 3 + 7 + 2 + 1 + 2 = 15. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 15 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "3 + 7 + 2 + 1 + 2",
"computed": 15
},
"found_expr": "3 + 7 + 2 + 1 + 2"
} | rich |
506aceff7e2821ef0ec95ac5d0bc83b5a21bdd13ab383995ab0225a9cb2eb5bc | NN_008-da606960 | natural_numbers | What is the multiplication of the digits of 44555? | Problem (NN_008): What is the multiplication of the digits of 44555? Step 1: Known: num=44555 Step 2: Approach: Digit sum of 44555 = 4 + 4 + 5 + 5 + 5 = 23. Step 3: Compute and conclude. | 23 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "4 + 4 + 5 + 5 + 5",
"computed": 23
},
"found_expr": "4 + 4 + 5 + 5 + 5"
} | rich |
514b2b73dc3b27ea2233851ba0920fec2f9d8c9e0a9752a96399af2be208b3bb | NN_011-033b4c0d | natural_numbers | How many trailing zeros are there in 59! (factorial)? | Problem (NN_011): How many trailing zeros are there in 59! (factorial)? Step 1: Known: n=59 Step 2: Approach: Digit sum of 59 = 5 + 9 = 14. Step 3: Compute and conclude. | 14 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "5 + 9",
"computed": 14
},
"found_expr": "5 + 9"
} | rich |
d114d8062c783ea84225628beffed54c2243d91723701b721dc038af57d2db84 | NN_006-0dac95aa | natural_numbers | What digit appears in the ones place of 29228? | Problem (NN_006): What digit appears in the ones place of 29228? Known: num=29228 Approach: Digit sum of 29228 = 2 + 9 + 2 + 2 + 8 = 23. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 23 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "2 + 9 + 2 + 2 + 8",
"computed": 23
},
"found_expr": "2 + 9 + 2 + 2 + 8"
} | rich |
007e444d2f0f79335026574e9060eb57667012ecaec5872cbb0d96a5b52e4e4c | NN_007-4814223e | natural_numbers | Count the even numbers in the interval [1,20]. | Goal: compute value for template NN_007. Givens: L=1, R=20 Using expression: ((R//2) - ((L-1)//2)) Substitute values: ((20//2) - ((1-1)//2)) Compute result → 10. Therefore the final answer is 10. | 10 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((20//2) - ((1-1)//2))",
"computed": 10
},
"found_expr": "((20//2) - ((1-1)//2))"
} | minimal |
6ed75e0b06fe43d0437fec9ca9db7b1a81556f563dd68dda7b5a0645c68ffa9b | NN_011-cfb4ec2b | natural_numbers | Compute the exponent of 10 in the prime factorization of 77!. | Problem (NN_011): Compute the exponent of 10 in the prime factorization of 77!. Step 1: Known: n=77 Step 2: Approach: Digit sum of 77 = 7 + 7 = 14. Step 3: Compute and conclude. | 14 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "7 + 7",
"computed": 14
},
"found_expr": "7 + 7"
} | rich |
9f2f125fa77b3cc2a32af1eb9e72e7234fd672f9ef5c04fc8ce2abee1ba11f51 | NN_005-1aab0a5a | natural_numbers | How many integers between 65 and 390 (inclusive) are divisible by 19? | Goal: compute value for template NN_005. Givens: L=65, R=390, k=19 Using expression: ((R//k) - ((L-1)//k)) Substitute values: ((390//19) - ((65-1)//19)) Compute result → 17. Therefore the final answer is 17. | 17 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((390//19) - ((65-1)//19))",
"computed": 17
},
"found_expr": "((390//19) - ((65-1)//19))"
} | minimal |
5619af13c167b7b90ea79ffc59f7022d7335f5d4c0102f1ed3cdab3a2c292660 | NN_012-d7326806 | natural_numbers | What is the digit-range (max minus min digit) of 64248? | Problem (NN_012): What is the digit-range (max minus min digit) of 64248? Known: num=64248 Approach: Digit sum of 64248 = 6 + 4 + 2 + 4 + 8 = 24. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 24 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "6 + 4 + 2 + 4 + 8",
"computed": 24
},
"found_expr": "6 + 4 + 2 + 4 + 8"
} | rich |
651ac212c3409fa216ee98fbb4ffff0161334bb0fb527704225964caca0dc1c6 | NN_007-4ffdb529 | natural_numbers | Between 1 and 3, inclusive, how many numbers are even? | Goal: compute value for template NN_007. Givens: L=1, R=3 Using expression: ((R//2) - ((L-1)//2)) Substitute values: ((3//2) - ((1-1)//2)) Compute result → 1. Therefore the final answer is 1. | 1 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((3//2) - ((1-1)//2))",
"computed": 1
},
"found_expr": "((3//2) - ((1-1)//2))"
} | minimal |
8d202abd709d9c09cfd3f52adba9be8eaf45fcb4fe36a307a28d71a697a3dfe8 | NN_002-147264d3 | natural_numbers | Compute the sum of 6 consecutive natural numbers starting at 4. | Goal: compute value for template NN_002. Givens: a=4, n=6 Using expression: ((n*(2*a + (n-1)*1))//2) Substitute values: ((6*(2*4 + (6-1)*1))//2) Compute result → 39. Therefore the final answer is 39. | 39 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((6*(2*4 + (6-1)*1))//2)",
"computed": 39
},
"found_expr": "((6*(2*4 + (6-1)*1))//2)"
} | minimal |
e747ca66803bd4718eb8a1ca76fe7388fe4d11f5448a760dd719023615f72da6 | NN_003-f6279c9e | natural_numbers | What is the sum of digits of the number 83174? | Problem (NN_003): What is the sum of digits of the number 83174? Known: num=83174 Approach: Digit sum of 83174 = 8 + 3 + 1 + 7 + 4 = 23. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 23 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "8 + 3 + 1 + 7 + 4",
"computed": 23
},
"found_expr": "8 + 3 + 1 + 7 + 4"
} | rich |
b6642ac216202f0490103ef66e3af315d1c4d2e5324876d3011f1b1329750564 | NN_011-90c7036d | natural_numbers | How many trailing zeros are there in 55! (factorial)? | Problem (NN_011): How many trailing zeros are there in 55! (factorial)? Step 1: Known: n=55 Step 2: Approach: Digit sum of 55 = 5 + 5 = 10. Step 3: Compute and conclude. | 10 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "5 + 5",
"computed": 10
},
"found_expr": "5 + 5"
} | rich |
08eeb2cd9e7bad29854b4fcbc3bdb9b9ab021fb593d5d4bf13dcfbd5815f51bf | NN_005-956f4638 | natural_numbers | Find the count of multiples of 12 in the interval [42,743]. | Goal: compute value for template NN_005. Givens: L=42, R=743, k=12 Using expression: ((R//k) - ((L-1)//k)) Substitute values: ((743//12) - ((42-1)//12)) Compute result → 58. Therefore the final answer is 58. | 58 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((743//12) - ((42-1)//12))",
"computed": 58
},
"found_expr": "((743//12) - ((42-1)//12))"
} | minimal |
bef85cb875c47be740f0a67b0bfdf1fb543bad53b88f31e96419c9087bc3d975 | NN_008-e4388e71 | natural_numbers | Compute the product of the decimal digits of 718. | Problem (NN_008): Compute the product of the decimal digits of 718. Step 1: Known: num=718 Step 2: Approach: Digit sum of 718 = 7 + 1 + 8 = 16. Step 3: Compute and conclude. | 16 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "7 + 1 + 8",
"computed": 16
},
"found_expr": "7 + 1 + 8"
} | rich |
75f0a2e35bd67976589e3afce09090373264a9bc1e18e815424794990a13993f | NN_006-a4591181 | natural_numbers | Find the units place digit of the number 31245. | Problem (NN_006): Find the units place digit of the number 31245. Known: num=31245 Approach: Digit sum of 31245 = 3 + 1 + 2 + 4 + 5 = 15. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 15 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "3 + 1 + 2 + 4 + 5",
"computed": 15
},
"found_expr": "3 + 1 + 2 + 4 + 5"
} | rich |
bad88ee4b255b878cb9a161c833a80c79ab7e09cb9bdfc614d5805508b8cd586 | NN_011-d590f2d6 | natural_numbers | How many trailing zeros are there in 11! (factorial)? | Problem (NN_011): How many trailing zeros are there in 11! (factorial)? Step 1: Known: n=11 Step 2: Approach: Digit sum of 11 = 1 + 1 = 2. Step 3: Compute and conclude. | 2 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "1 + 1",
"computed": 2
},
"found_expr": "1 + 1"
} | rich |
b737c62d319a5e218cad792b6400940bd77415eb6c32d7944077ac9cddfb907f | NN_005-c9b855cf | natural_numbers | Between 10 and 26, how many numbers are multiples of 4? | Goal: compute value for template NN_005. Givens: L=10, R=26, k=4 Using expression: ((R//k) - ((L-1)//k)) Substitute values: ((26//4) - ((10-1)//4)) Compute result → 4. Therefore the final answer is 4. | 4 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((26//4) - ((10-1)//4))",
"computed": 4
},
"found_expr": "((26//4) - ((10-1)//4))"
} | minimal |
30d494d1dc81e723b3796cd0cf8789ff00d0d430c0ecf00749be588e8e42cfba | NN_005-a14b3206 | natural_numbers | How many integers between 356 and 6161 (inclusive) are divisible by 27? | Goal: compute value for template NN_005. Givens: L=356, R=6161, k=27 Using expression: ((R//k) - ((L-1)//k)) Substitute values: ((6161//27) - ((356-1)//27)) Compute result → 215. Therefore the final answer is 215. | 215 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((6161//27) - ((356-1)//27))",
"computed": 215
},
"found_expr": "((6161//27) - ((356-1)//27))"
} | minimal |
5be25eec5424f571d589bacced6d779b265bd738d99c5e5120ea9fd0ce05b510 | NN_005-c6ac6f73 | natural_numbers | How many integers between 4 and 27 (inclusive) are divisible by 4? | Goal: compute value for template NN_005. Givens: L=4, R=27, k=4 Using expression: ((R//k) - ((L-1)//k)) Substitute values: ((27//4) - ((4-1)//4)) Compute result → 6. Therefore the final answer is 6. | 6 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((27//4) - ((4-1)//4))",
"computed": 6
},
"found_expr": "((27//4) - ((4-1)//4))"
} | minimal |
22f87d8a18069acec25cd1152b55168a233f42dd2c2f8671144853ff6ec3af40 | NN_012-7cf7b831 | natural_numbers | Find the difference between the largest and smallest digit of 944. | Problem (NN_012): Find the difference between the largest and smallest digit of 944. Known: num=944 Approach: Digit sum of 944 = 9 + 4 + 4 = 17. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 17 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "9 + 4 + 4",
"computed": 17
},
"found_expr": "9 + 4 + 4"
} | rich |
c72b886ac2a917075c3a623f32d229a7fb570dead8d1b8d705806cd33353b4a9 | NN_008-cb44218c | natural_numbers | Find the product of all digits in 1816. | Problem (NN_008): Find the product of all digits in 1816. Step 1: Known: num=1816 Step 2: Approach: Digit sum of 1816 = 1 + 8 + 1 + 6 = 16. Step 3: Compute and conclude. | 16 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "1 + 8 + 1 + 6",
"computed": 16
},
"found_expr": "1 + 8 + 1 + 6"
} | rich |
bbdea6073b9995eece3ddccabad59307446663897eaf95ce847ed247ebbef099 | NN_012-467d5135 | natural_numbers | Find the difference between the largest and smallest digit of 21441. | Problem (NN_012): Find the difference between the largest and smallest digit of 21441. Known: num=21441 Approach: Digit sum of 21441 = 2 + 1 + 4 + 4 + 1 = 12. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 12 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "2 + 1 + 4 + 4 + 1",
"computed": 12
},
"found_expr": "2 + 1 + 4 + 4 + 1"
} | rich |
072bb2990cc72180512c38913fef2ad92ccf8dedd4a442be04cab2b49c490b0b | NN_006-17bb23cd | natural_numbers | Find the units place digit of the number 135. | Problem (NN_006): Find the units place digit of the number 135. Known: num=135 Approach: Digit sum of 135 = 1 + 3 + 5 = 9. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 9 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "1 + 3 + 5",
"computed": 9
},
"found_expr": "1 + 3 + 5"
} | rich |
df2fc132f5558cc97bb417315bea4f9fe8770e3296152a67667b46a03462b01d | NN_003-9e75df95 | natural_numbers | Compute the digit-sum of 915. | Problem (NN_003): Compute the digit-sum of 915. Known: num=915 Approach: Digit sum of 915 = 9 + 1 + 5 = 15. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 15 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "9 + 1 + 5",
"computed": 15
},
"found_expr": "9 + 1 + 5"
} | rich |
11761e9694ecbf528039949cade1f6d48977e18ef66859222fb174a54c9f74d2 | NN_005-19beffc3 | natural_numbers | Between 89 and 362, how many numbers are multiples of 11? | Goal: compute value for template NN_005. Givens: L=89, R=362, k=11 Using expression: ((R//k) - ((L-1)//k)) Substitute values: ((362//11) - ((89-1)//11)) Compute result → 24. Therefore the final answer is 24. | 24 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((362//11) - ((89-1)//11))",
"computed": 24
},
"found_expr": "((362//11) - ((89-1)//11))"
} | minimal |
f4d6eae8276d82ff855bd64e9e4da01050b4f42f9b9d136f651c72993a595ea5 | NN_002-55242578 | natural_numbers | Compute the sum of 93 consecutive natural numbers starting at 628. | Goal: compute value for template NN_002. Givens: a=628, n=93 Using expression: ((n*(2*a + (n-1)*1))//2) Substitute values: ((93*(2*628 + (93-1)*1))//2) Compute result → 62682. Therefore the final answer is 62682. | 62,682 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((93*(2*628 + (93-1)*1))//2)",
"computed": 62682
},
"found_expr": "((93*(2*628 + (93-1)*1))//2)"
} | minimal |
39e3805e939ed4c77851adc43d395cafadb3ca709414b88d8f10a3bbbb6c1108 | NN_005-6114c522 | natural_numbers | Find the count of multiples of 14 in the interval [28,483]. | Goal: compute value for template NN_005. Givens: L=28, R=483, k=14 Using expression: ((R//k) - ((L-1)//k)) Substitute values: ((483//14) - ((28-1)//14)) Compute result → 33. Therefore the final answer is 33. | 33 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((483//14) - ((28-1)//14))",
"computed": 33
},
"found_expr": "((483//14) - ((28-1)//14))"
} | minimal |
b902e0f60dc01f1dccf79a9b21dc56c52e31b0f1c063726dae90e914ff5ed912 | NN_012-75f962b7 | natural_numbers | What is the digit-range (max minus min digit) of 736? | Problem (NN_012): What is the digit-range (max minus min digit) of 736? Known: num=736 Approach: Digit sum of 736 = 7 + 3 + 6 = 16. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 16 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "7 + 3 + 6",
"computed": 16
},
"found_expr": "7 + 3 + 6"
} | rich |
db594d873aa845908688edb4041ded58ba2f118ae98c3678c84de6279fec0f00 | NN_007-75a11534 | natural_numbers | Count the even numbers in the interval [32,104]. | Goal: compute value for template NN_007. Givens: L=32, R=104 Using expression: ((R//2) - ((L-1)//2)) Substitute values: ((104//2) - ((32-1)//2)) Compute result → 37. Therefore the final answer is 37. | 37 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((104//2) - ((32-1)//2))",
"computed": 37
},
"found_expr": "((104//2) - ((32-1)//2))"
} | minimal |
c49571a3353d8b05c6ab90e33cd9bea94c5351407288c8b967b38209c616a47f | NN_002-cb080cfd | natural_numbers | Compute the sum of 5 consecutive natural numbers starting at 38. | Goal: compute value for template NN_002. Givens: a=38, n=5 Using expression: ((n*(2*a + (n-1)*1))//2) Substitute values: ((5*(2*38 + (5-1)*1))//2) Compute result → 200. Therefore the final answer is 200. | 200 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((5*(2*38 + (5-1)*1))//2)",
"computed": 200
},
"found_expr": "((5*(2*38 + (5-1)*1))//2)"
} | minimal |
19c6e19665b0f5b6fb1e1b6593ea549ebe48ca365f8e8a5ae9c876fa52104655 | NN_009-df69dac9 | natural_numbers | From the first 10 natural numbers, how many unordered pairs can be selected? | Goal: compute value for template NN_009. Givens: n=10 Using expression: (n*(n-1))//2 Substitute values: (10*(10-1))//2 Compute result → 45. Therefore the final answer is 45. | 45 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "(10*(10-1))//2",
"computed": 45
},
"found_expr": "(10*(10-1))//2"
} | minimal |
609718f48b0f2aeb72708e430bfdf5f44bc5f5ce236dafcb483d9bce80f2964c | NN_001-f4dd9263 | natural_numbers | What is the sum of all natural numbers from 1 to 24 inclusive? | Goal: compute value for template NN_001. Givens: n=24 Using expression: (n*(n+1))//2 Substitute values: (24*(24+1))//2 Compute result → 300. Therefore the final answer is 300. | 300 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "(24*(24+1))//2",
"computed": 300
},
"found_expr": "(24*(24+1))//2"
} | minimal |
7b0c37179fb44c0b615e5264428966fb2fe89749a2e3d8d39ed42f7997eb913b | NN_005-5d153210 | natural_numbers | Find the count of multiples of 4 in the interval [57,172]. | Goal: compute value for template NN_005. Givens: L=57, R=172, k=4 Using expression: ((R//k) - ((L-1)//k)) Substitute values: ((172//4) - ((57-1)//4)) Compute result → 29. Therefore the final answer is 29. | 29 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((172//4) - ((57-1)//4))",
"computed": 29
},
"found_expr": "((172//4) - ((57-1)//4))"
} | minimal |
ddf67a92e7d85d7e9abdcdf5d732e1e4bb22889ee7d691ddcda57b3286064c01 | NN_008-a45ec5ec | natural_numbers | Find the product of all digits in 43987. | Problem (NN_008): Find the product of all digits in 43987. Step 1: Known: num=43987 Step 2: Approach: Digit sum of 43987 = 4 + 3 + 9 + 8 + 7 = 31. Step 3: Compute and conclude. | 31 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "4 + 3 + 9 + 8 + 7",
"computed": 31
},
"found_expr": "4 + 3 + 9 + 8 + 7"
} | rich |
390265009758744b4d673fc1ef465c40b2bb68f7d672f46c64048f1623f35834 | NN_003-48924dd4 | natural_numbers | Find the sum of all decimal digits in 84049. | Problem (NN_003): Find the sum of all decimal digits in 84049. Known: num=84049 Approach: Digit sum of 84049 = 8 + 4 + 0 + 4 + 9 = 25. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 25 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "8 + 4 + 0 + 4 + 9",
"computed": 25
},
"found_expr": "8 + 4 + 0 + 4 + 9"
} | rich |
8a9842af29e89109456bb135f694abcf8781b6b9a5f4b558a0d9d4d994760e21 | NN_005-fceb0c11 | natural_numbers | How many integers between 2 and 44 (inclusive) are divisible by 3? | Goal: compute value for template NN_005. Givens: L=2, R=44, k=3 Using expression: ((R//k) - ((L-1)//k)) Substitute values: ((44//3) - ((2-1)//3)) Compute result → 14. Therefore the final answer is 14. | 14 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((44//3) - ((2-1)//3))",
"computed": 14
},
"found_expr": "((44//3) - ((2-1)//3))"
} | minimal |
5f67849379ce3934b1e55e66fe0ed4cb0ee2b7089a1ad0ceb265a27c3ccf801e | NN_007-94c66697 | natural_numbers | Between 1 and 12, inclusive, how many numbers are even? | Goal: compute value for template NN_007. Givens: L=1, R=12 Using expression: ((R//2) - ((L-1)//2)) Substitute values: ((12//2) - ((1-1)//2)) Compute result → 6. Therefore the final answer is 6. | 6 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((12//2) - ((1-1)//2))",
"computed": 6
},
"found_expr": "((12//2) - ((1-1)//2))"
} | minimal |
05476a80069c2daba767953180a12674099a8d73e9692c44f907ac448231a5f8 | NN_003-b86e0844 | natural_numbers | Find the sum of all decimal digits in 32448. | Problem (NN_003): Find the sum of all decimal digits in 32448. Known: num=32448 Approach: Digit sum of 32448 = 3 + 2 + 4 + 4 + 8 = 21. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 21 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "3 + 2 + 4 + 4 + 8",
"computed": 21
},
"found_expr": "3 + 2 + 4 + 4 + 8"
} | rich |
18c3b3d5ae9067d3f80fe30aefb676d9f52e27a97a846098317543ff15c45c75 | NN_001-58a6a0e0 | natural_numbers | Compute the sum of the first 6 natural numbers. | Goal: compute value for template NN_001. Givens: n=6 Using expression: (n*(n+1))//2 Substitute values: (6*(6+1))//2 Compute result → 21. Therefore the final answer is 21. | 21 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "(6*(6+1))//2",
"computed": 21
},
"found_expr": "(6*(6+1))//2"
} | minimal |
4f9b0e56e79f3d6614ed708687a02793374f4c90a0fd1525ad78a86dc47fe8b5 | NN_001-54b39b78 | natural_numbers | What is the sum of all natural numbers from 1 to 390 inclusive? | Goal: compute value for template NN_001. Givens: n=390 Using expression: (n*(n+1))//2 Substitute values: (390*(390+1))//2 Compute result → 76245. Therefore the final answer is 76245. | 76,245 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "(390*(390+1))//2",
"computed": 76245
},
"found_expr": "(390*(390+1))//2"
} | minimal |
afac36870638c1e3fbc296a571a3e059045a735b2b1e177a97c792f350a1648e | NN_002-b67aaa82 | natural_numbers | Compute the sum of 19 consecutive natural numbers starting at 98. | Goal: compute value for template NN_002. Givens: a=98, n=19 Using expression: ((n*(2*a + (n-1)*1))//2) Substitute values: ((19*(2*98 + (19-1)*1))//2) Compute result → 2033. Therefore the final answer is 2033. | 2,033 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((19*(2*98 + (19-1)*1))//2)",
"computed": 2033
},
"found_expr": "((19*(2*98 + (19-1)*1))//2)"
} | minimal |
037bea8b08cd82ec7efe860b4e9a690045f66f6390246496636c0c375a755d11 | NN_001-a8998566 | natural_numbers | What is the sum of all natural numbers from 1 to 139 inclusive? | Goal: compute value for template NN_001. Givens: n=139 Using expression: (n*(n+1))//2 Substitute values: (139*(139+1))//2 Compute result → 9730. Therefore the final answer is 9730. | 9,730 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "(139*(139+1))//2",
"computed": 9730
},
"found_expr": "(139*(139+1))//2"
} | minimal |
a7f6dfbaa2aed04d6c0513400e817f02a78e10c336a33b135ee69e16a5512aa2 | NN_011-097d259b | natural_numbers | Compute the exponent of 10 in the prime factorization of 34!. | Problem (NN_011): Compute the exponent of 10 in the prime factorization of 34!. Step 1: Known: n=34 Step 2: Approach: Digit sum of 34 = 3 + 4 = 7. Step 3: Compute and conclude. | 7 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "3 + 4",
"computed": 7
},
"found_expr": "3 + 4"
} | rich |
2effbc4fbf45441e046482f9773ab072cca27666ae67ea4addb78cafa26022c5 | NN_003-bf8592ac | natural_numbers | What is the sum of digits of the number 6486? | Problem (NN_003): What is the sum of digits of the number 6486? Known: num=6486 Approach: Digit sum of 6486 = 6 + 4 + 8 + 6 = 24. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 24 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "6 + 4 + 8 + 6",
"computed": 24
},
"found_expr": "6 + 4 + 8 + 6"
} | rich |
7c64a4197cf51aa6c4e14aa31f88377ed8dbd175d47e8b4d5a1b9c75ff61a0cc | NN_003-f1243239 | natural_numbers | Find the sum of all decimal digits in 459. | Problem (NN_003): Find the sum of all decimal digits in 459. Known: num=459 Approach: Digit sum of 459 = 4 + 5 + 9 = 18. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 18 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "4 + 5 + 9",
"computed": 18
},
"found_expr": "4 + 5 + 9"
} | rich |
de2f08deef661e3d175c98c333addede6f90333efd7fbf17fa0e5bdcb94c81bc | NN_006-78c0b3a3 | natural_numbers | Find the units place digit of the number 54999. | Problem (NN_006): Find the units place digit of the number 54999. Known: num=54999 Approach: Digit sum of 54999 = 5 + 4 + 9 + 9 + 9 = 36. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 36 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "5 + 4 + 9 + 9 + 9",
"computed": 36
},
"found_expr": "5 + 4 + 9 + 9 + 9"
} | rich |
f4922e440b43fc0cd8c8d5c3756bea4d4c3214ea4daa9f991886aa36e354e72f | NN_007-e5d6b97c | natural_numbers | Count the even numbers in the interval [575,9960]. | Goal: compute value for template NN_007. Givens: L=575, R=9960 Using expression: ((R//2) - ((L-1)//2)) Substitute values: ((9960//2) - ((575-1)//2)) Compute result → 4693. Therefore the final answer is 4693. | 4,693 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((9960//2) - ((575-1)//2))",
"computed": 4693
},
"found_expr": "((9960//2) - ((575-1)//2))"
} | minimal |
3bcd4a6c1ce107a9b2a0e20b048bc15ae74f12ac5d7d1286a16ec8716a43a039 | NN_006-339e8ff1 | natural_numbers | What is the last (units) digit of 434? | Problem (NN_006): What is the last (units) digit of 434? Known: num=434 Approach: Digit sum of 434 = 4 + 3 + 4 = 11. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 11 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "4 + 3 + 4",
"computed": 11
},
"found_expr": "4 + 3 + 4"
} | rich |
2075358cc863168f0da78341c95b54e331cb49bf4e779fbad932600117764c70 | NN_003-c5151de8 | natural_numbers | What is the sum of digits of the number 45397? | Problem (NN_003): What is the sum of digits of the number 45397? Known: num=45397 Approach: Digit sum of 45397 = 4 + 5 + 3 + 9 + 7 = 28. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 28 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "4 + 5 + 3 + 9 + 7",
"computed": 28
},
"found_expr": "4 + 5 + 3 + 9 + 7"
} | rich |
688ac422e8b319d70aad51b7c5fdff045aa02a6f23e0084917b83fdb98a03862 | NN_007-7d7e5c09 | natural_numbers | Count the even numbers in the interval [1,16]. | Goal: compute value for template NN_007. Givens: L=1, R=16 Using expression: ((R//2) - ((L-1)//2)) Substitute values: ((16//2) - ((1-1)//2)) Compute result → 8. Therefore the final answer is 8. | 8 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "((16//2) - ((1-1)//2))",
"computed": 8
},
"found_expr": "((16//2) - ((1-1)//2))"
} | minimal |
d8a516b838f76cacd99bc53901157a1dd1bfb2f518b3068a15e739f625989c90 | NN_012-b06a84bd | natural_numbers | Compute (max digit) - (min digit) for the decimal digits of 90472. | Problem (NN_012): Compute (max digit) - (min digit) for the decimal digits of 90472. Known: num=90472 Approach: Digit sum of 90472 = 9 + 0 + 4 + 7 + 2 = 22. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 22 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "9 + 0 + 4 + 7 + 2",
"computed": 22
},
"found_expr": "9 + 0 + 4 + 7 + 2"
} | rich |
4dc9df16bbbbca21e0638fd4f05672e9cc4ef90716d27c0a196205ef7aaf14a0 | NN_003-c9ecc4c8 | natural_numbers | Find the sum of all decimal digits in 49920. | Problem (NN_003): Find the sum of all decimal digits in 49920. Known: num=49920 Approach: Digit sum of 49920 = 4 + 9 + 9 + 2 + 0 = 24. Calculation: show intermediate steps as below. Conclusion: the final numeric answer follows. | 24 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "4 + 9 + 9 + 2 + 0",
"computed": 24
},
"found_expr": "4 + 9 + 9 + 2 + 0"
} | rich |
29ac285d9ea989138c9f24646f12e6212774019adbde2aaf9c9a32f4bfbd29f0 | NN_001-bb6c5504 | natural_numbers | Compute the sum of the first 400 natural numbers. | Goal: compute value for template NN_001. Givens: n=400 Using expression: (n*(n+1))//2 Substitute values: (400*(400+1))//2 Compute result → 80200. Therefore the final answer is 80200. | 80,200 | aimo3-dataset/chapters/natural_numbers/filtered/converted_natural_numbers.jsonl | {
"consistent": true,
"reason": {
"method": "expr_eval",
"expr": "(400*(400+1))//2",
"computed": 80200
},
"found_expr": "(400*(400+1))//2"
} | minimal |
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