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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 dataset

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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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