conversation listlengths 2 2 | seed int64 68.2k 199M | task_id int64 1.38M 900M | task_metadata dict | task_type stringclasses 8
values | usage dict |
|---|---|---|---|---|---|
[
{
"content": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: }}>⟩]]]}\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence... | 116,120,358 | 516,120,358 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 8,
"full_sequence": "{[[[⟨<{{}}>⟩]]]}",
"generation_error": null,
"generation_failed": null,
"generation_trace... | dyck_language2 | {
"completion_tokens": 538,
"completion_tokens_details": null,
"prompt_tokens": 81,
"prompt_tokens_details": null,
"total_tokens": 619
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 7,269,383 | 807,269,383 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[]()[()()]",
"error_indices": [
6,
10
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"gene... | dyck_language_reasoning_errors | {
"completion_tokens": 193,
"completion_tokens_details": null,
"prompt_tokens": 252,
"prompt_tokens_details": null,
"total_tokens": 445
} |
[
{
"content": "Fill in the blank:\n\n_____ + []()()<>()[]}<><>}][]>)[]]{})))]>)]<> = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`.",
"reasoning_content": null... | 56,101,189 | 456,101,189 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 13,
"full_sequence": "[(<[((([(<[{{[]()()<>()[]}<><>}][]>)[]]{})))]>)]<>",
"generation_error": null,
"generation... | dyck_language2 | {
"completion_tokens": 1141,
"completion_tokens_details": null,
"prompt_tokens": 76,
"prompt_tokens_details": null,
"total_tokens": 1217
} |
[
{
"content": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: ⟩[]<>]>⟧>}]})⟧)}⟧]⟧⟩>\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full bala... | 33,638,404 | 433,638,404 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 17,
"full_sequence": "<⟨⟦[⟦{(⟦({[{<⟦<[⟨⟩[]<>]>⟧>}]})⟧)}⟧]⟧⟩>",
"generation_error": null,
"generation_failed": nu... | dyck_language2 | {
"completion_tokens": 1221,
"completion_tokens_details": null,
"prompt_tokens": 92,
"prompt_tokens_details": null,
"total_tokens": 1313
} |
[
{
"content": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: )})[]}))\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPlease p... | 197,420,771 | 597,420,771 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 6,
"full_sequence": "(({({()})[]}))",
"generation_error": null,
"generation_failed": null,
"generation_traceba... | dyck_language2 | {
"completion_tokens": 439,
"completion_tokens_details": null,
"prompt_tokens": 84,
"prompt_tokens_details": null,
"total_tokens": 523
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 11,228,580 | 811,228,580 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[<>[]()<>[]][]{{}}<(<()<>>)[]>",
"error_indices": [
7,
23,
30,
31,
32
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error"... | dyck_language_reasoning_errors | {
"completion_tokens": 481,
"completion_tokens_details": null,
"prompt_tokens": 480,
"prompt_tokens_details": null,
"total_tokens": 961
} |
[
{
"content": "Study the following logical statements:\n\nA. not ((-3 * 9 * -2 * -10) <= (-8 * 8 * 3 * -7))\nB. not not ((4 * -6 * 10 * -4) > (6 - -20))\nC. (((Gold is a liquid at room temperature.) and ((12 * -3) <= (-11 + -7))) or ((Oil is a liquid at room temperature.) or (The 1968 Olympics were held in Rome.... | 74,388,075 | 674,388,075 | {
"closing_sequence": null,
"depth": 3,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"not ((-3 * 9 * -2 * -10) <= (-8 * 8 * 3 * -7))",
"False"
],
[
"not not ((4 * -6 * 10 * -4) > (6 - -20))",
... | boolean_expressions | {
"completion_tokens": 761,
"completion_tokens_details": null,
"prompt_tokens": 324,
"prompt_tokens_details": null,
"total_tokens": 1085
} |
[
{
"content": "Define ○, the rules are as follows:\non the real number field, x ○ y = (y) * x.\nThe precedence of operations: ** > * = / = % > + = - = ○。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 7 % 1 ○... | 22,917,703 | 222,917,703 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "7 % 1 ○ 6",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback... | operation | {
"completion_tokens": 266,
"completion_tokens_details": null,
"prompt_tokens": 98,
"prompt_tokens_details": null,
"total_tokens": 364
} |
[
{
"content": "Q: What opening brackets should precede \"⟩)⟩\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`.",
"reasoning... | 194,607,815 | 594,607,815 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 3,
"full_sequence": "⟨(⟨⟩)⟩",
"generation_error": null,
"generation_failed": null,
"generation_traceback": nul... | dyck_language2 | {
"completion_tokens": 304,
"completion_tokens_details": null,
"prompt_tokens": 69,
"prompt_tokens_details": null,
"total_tokens": 373
} |
[
{
"content": "Given the following boolean expressions:\n\nA. not ((((-17 - -18) > (35 % 5)) and (The capital of Switzerland is Oslo.)) and ((The Great Wall of China was built in one year.) or (Wood is a solid at room temperature.)))\nB. ((The 1980 Olympics were held in Moscow.) or ((19 is a prime number.) or ((... | 28,845,518 | 628,845,518 | {
"closing_sequence": null,
"depth": 3,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"not ((((-17 - -18) > (35 % 5)) and (The capital of Switzerland is Oslo.)) and ((The Great Wall of China was built in one year.) o... | boolean_expressions | {
"completion_tokens": 1150,
"completion_tokens_details": null,
"prompt_tokens": 476,
"prompt_tokens_details": null,
"total_tokens": 1626
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 59,437,993 | 859,437,993 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[]<{}><><[<()()<[][][]>[]>]>{}",
"error_indices": [
3,
16,
26,
28
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
... | dyck_language_reasoning_errors | {
"completion_tokens": 479,
"completion_tokens_details": null,
"prompt_tokens": 506,
"prompt_tokens_details": null,
"total_tokens": 985
} |
[
{
"content": "Q: What opening brackets should precede \"⟩)}⟩>⟨⟩}}⟩⟨⟩⟩[]⟩]>]{}}⟨⟩<>{}{}()<>⟨⟩[]\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backti... | 14,655,426 | 414,655,426 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 14,
"full_sequence": "{[<[⟨⟨⟨{{<⟨{(⟨⟩)}⟩>⟨⟩}}⟩⟨⟩⟩[]⟩]>]{}}⟨⟩<>{}{}()<>⟨⟩[]",
"generation_error": null,
"generati... | dyck_language2 | {
"completion_tokens": 1311,
"completion_tokens_details": null,
"prompt_tokens": 91,
"prompt_tokens_details": null,
"total_tokens": 1402
} |
[
{
"content": "Let S = \"⟩}>]}⟩)⟩⟩>]})}⟩]}}⟩}\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
{
"conte... | 132,610,186 | 532,610,186 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 20,
"full_sequence": "{⟨{{[⟨{({[<⟨⟨(⟨{[<{⟨⟩}>]}⟩)⟩⟩>]})}⟩]}}⟩}",
"generation_error": null,
"generation_failed": ... | dyck_language2 | {
"completion_tokens": 1417,
"completion_tokens_details": null,
"prompt_tokens": 78,
"prompt_tokens_details": null,
"total_tokens": 1495
} |
[
{
"content": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: )()}⟨⟩\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence) ... | 34,957,363 | 434,957,363 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 2,
"full_sequence": "{()()}⟨⟩",
"generation_error": null,
"generation_failed": null,
"generation_traceback": n... | dyck_language2 | {
"completion_tokens": 303,
"completion_tokens_details": null,
"prompt_tokens": 81,
"prompt_tokens_details": null,
"total_tokens": 384
} |
[
{
"content": "Evaluate each expression below:\n\nA. not (((not not (((The 1912 Olympics were held in Stockholm.) or ((5 * -3 * -4 * -5) == (3 - 8))) or ((13 - -16) <= (25 % 10) <= (2 ** 3)))) and ((not not (The currency of Chile is the Real.)) and (((15 + 15) > (-17 - -2)) or ((1 ** 2) >= (31 % 6))))) or ((not ... | 70,754,210 | 670,754,210 | {
"closing_sequence": null,
"depth": 6,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"not (((not not (((The 1912 Olympics were held in Stockholm.) or ((5 * -3 * -4 * -5) == (3 - 8))) or ((13 - -16) <= (25 % 10) <= (... | boolean_expressions | {
"completion_tokens": 1577,
"completion_tokens_details": null,
"prompt_tokens": 695,
"prompt_tokens_details": null,
"total_tokens": 2272
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 93,181,487 | 893,181,487 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "(((()()))())",
"error_indices": [
7,
11,
14
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": nul... | dyck_language_reasoning_errors | {
"completion_tokens": 244,
"completion_tokens_details": null,
"prompt_tokens": 276,
"prompt_tokens_details": null,
"total_tokens": 520
} |
[
{
"content": "Define ♡, the rules are as follows:\non the real number field, x ♡ y = y * x + y.\nand ♢, the rules are as follows:\nwhen x is greater than y, x ♢ y = x + y;\notherwise, x ♢ y = x + abs(y).\nThe precedence of operations: ♡ = ♢ > ** > * = / = % > + = -。\nParentheses have the highest priority,... | 24,128,106 | 224,128,106 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "4 ♢ 7",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": n... | operation | {
"completion_tokens": 433,
"completion_tokens_details": null,
"prompt_tokens": 142,
"prompt_tokens_details": null,
"total_tokens": 575
} |
[
{
"content": "定义 ⊕，规则如下：\n当x是5的倍数时，x ⊕ y = y + y - y * y * x；\n其他情况下，x ⊕ y = 1 - 1 * y - y + x。\n和 ◇，规则如下：\n实数域上，x ◇ y = y - 3 ** x * x。\n和 □，规则如下：\n实数域上，x □ y = 2 - x - 3 ** y。\n运算优先级：□ > ** > * = / = % = ⊕ = ◇ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 10 ⊕ 6 ◇ 4\n请将最终答案填入\\boxed{}中。",
"reasoning_... | 31,703,022 | 231,703,022 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "10 ⊕ 6 ◇ 4",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_tracebac... | operation | {
"completion_tokens": 654,
"completion_tokens_details": null,
"prompt_tokens": 186,
"prompt_tokens_details": null,
"total_tokens": 840
} |
[
{
"content": "Fill in the blank:\n\n_____ + <>]}]]])}{}>>}} = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
... | 84,184,336 | 484,184,336 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 11,
"full_sequence": "{{<<{([[[{[<>]}]]])}{}>>}}",
"generation_error": null,
"generation_failed": null,
"gener... | dyck_language2 | {
"completion_tokens": 753,
"completion_tokens_details": null,
"prompt_tokens": 65,
"prompt_tokens_details": null,
"total_tokens": 818
} |
[
{
"content": "Fill in the blank:\n\n_____ + )])}>]}()][]{}{}()<> = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`.",
"reasoning_content": null,
"role": "us... | 4,376,049 | 404,376,049 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 8,
"full_sequence": "[{[<{([()])}>]}()][]{}{}()<>",
"generation_error": null,
"generation_failed": null,
"gene... | dyck_language2 | {
"completion_tokens": 679,
"completion_tokens_details": null,
"prompt_tokens": 67,
"prompt_tokens_details": null,
"total_tokens": 746
} |
[
{
"content": "Let S = \"⦄⟧)\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
{
"content": "`(⟦⦃⦄⟧)`",
... | 106,420,354 | 506,420,354 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 3,
"full_sequence": "(⟦⦃⦄⟧)",
"generation_error": null,
"generation_failed": null,
"generation_traceback": nul... | dyck_language2 | {
"completion_tokens": 313,
"completion_tokens_details": null,
"prompt_tokens": 67,
"prompt_tokens_details": null,
"total_tokens": 380
} |
[
{
"content": "Let S = \")⟨⟩⟩{}]⟨⟩><>]()⟧⟧)}⟧]⟧⦃⦄⟩⟨⟩<><>⟦⟧⟨⟩\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},... | 36,575,122 | 436,575,122 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 13,
"full_sequence": "⟨⟦[⟦{(⟦⟦[<[⟨()⟨⟩⟩{}]⟨⟩><>]()⟧⟧)}⟧]⟧⦃⦄⟩⟨⟩<><>⟦⟧⟨⟩",
"generation_error": null,
"generation_f... | dyck_language2 | {
"completion_tokens": 1246,
"completion_tokens_details": null,
"prompt_tokens": 93,
"prompt_tokens_details": null,
"total_tokens": 1339
} |
[
{
"content": "Fill in the blank:\n\n_____ + ⟩⟧>⟩⟩>⟧⦄]⟩ = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
... | 193,949,908 | 593,949,908 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 10,
"full_sequence": "⟨[⦃⟦<⟨⟨<⟦⟨⟩⟧>⟩⟩>⟧⦄]⟩",
"generation_error": null,
"generation_failed": null,
"generation_... | dyck_language2 | {
"completion_tokens": 736,
"completion_tokens_details": null,
"prompt_tokens": 69,
"prompt_tokens_details": null,
"total_tokens": 805
} |
[
{
"content": "定义 ▽，规则如下：\n当y是5的倍数时，x ▽ y = y + x + x；\n其他情况下，x ▽ y = (x + y * y)。\n运算优先级：** = ▽ > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 5\n请将最终答案填入\\boxed{}中。",
"reasoning_content": null,
"role": "user"
},
{
"content": "根据问题描述，表达式为“5”，该表达式仅包含一个数字，无任何运算符。因此，表达式的值即为5。\n\n\\boxed... | 95,423,666 | 295,423,666 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "5",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null,... | operation | {
"completion_tokens": 1481,
"completion_tokens_details": null,
"prompt_tokens": 109,
"prompt_tokens_details": null,
"total_tokens": 1590
} |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: [])}}))}}))\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- ... | 89,769,750 | 489,769,750 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 9,
"full_sequence": "(({{(({{([])}}))}}))",
"generation_error": null,
"generation_failed": null,
"generation_t... | dyck_language2 | {
"completion_tokens": 589,
"completion_tokens_details": null,
"prompt_tokens": 96,
"prompt_tokens_details": null,
"total_tokens": 685
} |
[
{
"content": "定义 ○，规则如下：\n当x和y的和是偶数时，x ○ y = x - 4 + 3 - y / y；\n其他情况下，x ○ y = x + y + 3 + (y * x)。\n运算优先级：○ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 4 ○ 7\n请将最终答案填入\\boxed{}中。",
"reasoning_content": null,
"role": "user"
},
{
"content": "根据规则：\n\n- 当 \\(x+y\\) 为偶数时，\\(x \\... | 46,938,911 | 246,938,911 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "4 ○ 7",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": n... | operation | {
"completion_tokens": 242,
"completion_tokens_details": null,
"prompt_tokens": 121,
"prompt_tokens_details": null,
"total_tokens": 363
} |
[
{
"content": "Q: What opening brackets should precede \">}⟨⟩){}>⟨⟩>⟩⟩<>⟩())>>()⟩⟩}⟩})>}}\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks li... | 109,821,444 | 509,821,444 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 20,
"full_sequence": "{{<({⟨{⟨⟨<<(⟨⟨⟨<<({<>}⟨⟩){}>⟨⟩>⟩⟩<>⟩())>>()⟩⟩}⟩})>}}",
"generation_error": null,
"generati... | dyck_language2 | {
"completion_tokens": 1595,
"completion_tokens_details": null,
"prompt_tokens": 86,
"prompt_tokens_details": null,
"total_tokens": 1681
} |
[
{
"content": "Given [8, 9, 11, 12, 13], use the operations ['+', '-', '*'] to obtain 100.\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there... | 61,597,983 | 161,597,983 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 4846,
"completion_tokens_details": null,
"prompt_tokens": 99,
"prompt_tokens_details": null,
"total_tokens": 4945
} |
[
{
"content": "Numbers: [1, 2, 4, 9], operators: ['+', '-'], target: 36.\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there is no solution, p... | 82,762,781 | 182,762,781 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 1767,
"completion_tokens_details": null,
"prompt_tokens": 91,
"prompt_tokens_details": null,
"total_tokens": 1858
} |
[
{
"content": "解决密码算术谜题：GFUU + G * TYU = YYYFY（其中GFUU是4位数、G是1位数、TYU是3位数、YYYFY是5位数），其中每个字母表示0-9之间的一个数字，不同字母代表不同数字。请计算出使等式成立的数字等式。 请在回答的最后一行使用以下格式：答案是 $YOUR_ANSWER。$YOUR_ANSWER 应该是替换为数字后的等式。",
"reasoning_content": null,
"role": "user"
},
{
"content": "根据密码算术谜题的条件，通过分析个位相加的模10关系，得出可能的(G, U)组合为(2,7)、... | 68,261,903 | 368,261,903 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": null,
"D": null,
"E": null,
"F": 5,
"G": 8,
"H": null,
"I": null,
"J": null,
"K": null,
"L": null,
"M": null,
"N": null,
"O": null,
"P": null,
... | cryptarithm | {
"completion_tokens": 4841,
"completion_tokens_details": null,
"prompt_tokens": 118,
"prompt_tokens_details": null,
"total_tokens": 4959
} |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: ⟩}>⟧>}]⦄)⟧⟩⟩}⟩\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\... | 118,868,519 | 518,868,519 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 14,
"full_sequence": "⟨{⟨⟨⟦(⦃[{<⟦<{⟨⟩}>⟧>}]⦄)⟧⟩⟩}⟩",
"generation_error": null,
"generation_failed": null,
"gen... | dyck_language2 | {
"completion_tokens": 988,
"completion_tokens_details": null,
"prompt_tokens": 106,
"prompt_tokens_details": null,
"total_tokens": 1094
} |
[
{
"content": "Here are some boolean expressions to evaluate:\n\nA. (((The 1936 Olympics were held in Athens.) and (not not (There are 30 days in May.)) and (New Zealand is in Oceania.)) or ((not (((-4 * 2 + -5 * -2) < (35 % 1)) or ((17 + 8) > (-4 * 12)))) and ((-20 - 5) <= (-2 - -2)))) or (not not (((-6 * -10 +... | 87,020,451 | 687,020,451 | {
"closing_sequence": null,
"depth": 5,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"(((The 1936 Olympics were held in Athens.) and (not not (There are 30 days in May.)) and (New Zealand is in Oceania.)) or ((not (... | boolean_expressions | {
"completion_tokens": 2654,
"completion_tokens_details": null,
"prompt_tokens": 1140,
"prompt_tokens_details": null,
"total_tokens": 3794
} |
[
{
"content": "解决密码算术谜题：ZOOE - QEIE - ZZIO + IIZQI = ZIEE（其中ZOOE是4位数、QEIE是4位数、ZZIO是4位数、IIZQI是5位数、ZIEE是4位数），其中每个字母表示0-9之间的一个数字，不同字母代表不同数字。请计算出使等式成立的数字等式。 请在回答的最后一行使用以下格式：答案是 $YOUR_ANSWER。$YOUR_ANSWER 应该是替换为数字后的等式。",
"reasoning_content": null,
"role": "user"
},
{
"content": "答案是 9665 - 2515 - 9916 ... | 79,281,357 | 379,281,357 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": null,
"D": null,
"E": 5,
"F": null,
"G": null,
"H": null,
"I": 1,
"J": null,
"K": null,
"L": null,
"M": null,
"N": null,
"O": 6,
"P": null,
... | cryptarithm | {
"completion_tokens": 7917,
"completion_tokens_details": null,
"prompt_tokens": 137,
"prompt_tokens_details": null,
"total_tokens": 8054
} |
[
{
"content": "Given: FFSFF - WDSD = SWSSF, where each letter represents a unique digit (FFSFF is a 5-digit number, WDSD is a 4-digit number, and SWSSF is a 5-digit number). Find the numeric equation that makes the equality valid. Please end your response in the last line with the following format: The answer is... | 52,861,572 | 352,861,572 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": null,
"D": 0,
"E": null,
"F": 2,
"G": null,
"H": null,
"I": null,
"J": null,
"K": null,
"L": null,
"M": null,
"N": null,
"O": null,
"P": null,
... | cryptarithm | {
"completion_tokens": 5390,
"completion_tokens_details": null,
"prompt_tokens": 104,
"prompt_tokens_details": null,
"total_tokens": 5494
} |
[
{
"content": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: ⟦⟧⦃⦄>}⦄)⟧⟩]⦄⟧>⦄>⟩\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced... | 45,134,263 | 445,134,263 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 13,
"full_sequence": "⟨<⦃<⟦⦃[⟨⟦(⦃{<⟦⟧⦃⦄>}⦄)⟧⟩]⦄⟧>⦄>⟩",
"generation_error": null,
"generation_failed": null,
"g... | dyck_language2 | {
"completion_tokens": 1054,
"completion_tokens_details": null,
"prompt_tokens": 99,
"prompt_tokens_details": null,
"total_tokens": 1153
} |
[
{
"content": "定义 ◎，规则如下：\n实数域上，x ◎ y = x - y - y / 2。\n和 ☆，规则如下：\n实数域上，x ☆ y = (x + y * 1 - y * y)。\n运算优先级：◎ > ☆ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 9 ☆ 2 / 5 ◎ 2\n请将最终答案填入\\boxed{}中。",
"reasoning_content": null,
"role": "user"
},
{
"content": "先根据运算优先级先算最高的 **◎**，再算 ... | 88,063,803 | 288,063,803 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "9 ☆ 2 / 5 ◎ 2",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_trace... | operation | {
"completion_tokens": 561,
"completion_tokens_details": null,
"prompt_tokens": 131,
"prompt_tokens_details": null,
"total_tokens": 692
} |
[
{
"content": "Sudoku Challenge:\n\n```\n2.81..763\n7169.3245\n.43...91.\n.8.5.9.2.\n32..6..57\n..5.28..9\n85.3.7..6\n9.4..2..1\n6.18..5.2\n```\n\nFill in the blanks ('.') following standard Sudoku rules. Output the complete solution grid wrapped in ``` marks.",
"reasoning_content": null,
"role": "user"
... | 18,373,414 | 718,373,414 | {
"closing_sequence": null,
"depth": null,
"difficulty": "easy",
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": nu... | sudoku | {
"completion_tokens": 4614,
"completion_tokens_details": null,
"prompt_tokens": 116,
"prompt_tokens_details": null,
"total_tokens": 4730
} |
[
{
"content": "Here are some boolean expressions to evaluate:\n\nA. ((not not ((Morocco is in Africa.) and ((19 * 3) != (8 * -6 - 10 * -3)))) or (not not ((The Earth revolves around the Sun.) or (The Great Wall of China was built in one year.)))) and (not ((41 % 9) <= (-7 * -13)))\nB. (not not ((-10 - 5) < (-17 ... | 86,126,022 | 686,126,022 | {
"closing_sequence": null,
"depth": 4,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"((not not ((Morocco is in Africa.) and ((19 * 3) != (8 * -6 - 10 * -3)))) or (not not ((The Earth revolves around the Sun.) or (T... | boolean_expressions | {
"completion_tokens": 2010,
"completion_tokens_details": null,
"prompt_tokens": 865,
"prompt_tokens_details": null,
"total_tokens": 2875
} |
[
{
"content": "Evaluate each expression below:\n\nA. ((not ((not not (138 is a perfect square.)) and (not not ((1 * 0) < (-4 * 5 * 5 * 5))))) and (not (2050 is a leap year.))) or (not ((not ((-5 * -8) != (2 + 8))) and (not not ((-20 * -4) < (-15 + 16))))) or (not not ((((6 + 18) != (12 * -13)) and ((The Moon orb... | 93,769,404 | 693,769,404 | {
"closing_sequence": null,
"depth": 5,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"((not ((not not (138 is a perfect square.)) and (not not ((1 * 0) < (-4 * 5 * 5 * 5))))) and (not (2050 is a leap year.))) or (no... | boolean_expressions | {
"completion_tokens": 2583,
"completion_tokens_details": null,
"prompt_tokens": 1108,
"prompt_tokens_details": null,
"total_tokens": 3691
} |
[
{
"content": "Here are some boolean expressions to evaluate:\n\nA. not ((((not ((2 * 3 - -8 * 9) >= (-6 * 8))) and ((10 * -15) != (14 * 1))) or (not not (not not (The chemical symbol for Platinum is Pt.)))) or ((not not (((-14 - -17) > (2 - -10)) and (Mercury is a gas at room temperature.))) and (not not (((-6 ... | 42,151,716 | 642,151,716 | {
"closing_sequence": null,
"depth": 5,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"not ((((not ((2 * 3 - -8 * 9) >= (-6 * 8))) and ((10 * -15) != (14 * 1))) or (not not (not not (The chemical symbol for Platinum ... | boolean_expressions | {
"completion_tokens": 1379,
"completion_tokens_details": null,
"prompt_tokens": 623,
"prompt_tokens_details": null,
"total_tokens": 2002
} |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary closing brackets.\n\nSequence: ⟨⟩((⟨⟨[]⟨[⟨[()][]()⟩()]⟩<>⟨⟩⟩⟩({⟨{{{}}()[][][{(({({\n\nRules:\n- Add only the closing brackets needed to match all unmatched opening brackets\n- Do not add any extra bracket pairs beyond wh... | 72,763,649 | 72,763,649 | {
"closing_sequence": "})}))}]}⟩})))",
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 13,
"full_sequence": "⟨⟩((⟨⟨[]⟨[⟨[()][]()⟩()]⟩<>⟨⟩⟩⟩({⟨{{{}}()[][][{(({({})}))}]}⟩})))",
"generation_er... | dyck_language | {
"completion_tokens": 1548,
"completion_tokens_details": null,
"prompt_tokens": 93,
"prompt_tokens_details": null,
"total_tokens": 1641
} |
[
{
"content": "Sudoku Challenge:\n\n```\n....82.1.\n51.967234\n6724....5\n85.1963..\n19.......\n.6...81.9\n...25396.\n.85..9.21\n.2..1..73\n```\n\nFill in the blanks ('.') following standard Sudoku rules. Output the complete solution grid wrapped in ``` marks.",
"reasoning_content": null,
"role": "user"
... | 40,601,653 | 740,601,653 | {
"closing_sequence": null,
"depth": null,
"difficulty": "easy",
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": nu... | sudoku | {
"completion_tokens": 6247,
"completion_tokens_details": null,
"prompt_tokens": 106,
"prompt_tokens_details": null,
"total_tokens": 6353
} |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: ]]])})}()()]()]())[]{}{}\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid... | 98,067,589 | 498,067,589 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 10,
"full_sequence": "([[{({([[[]]])})}()()]()]())[]{}{}",
"generation_error": null,
"generation_failed": null,
... | dyck_language2 | {
"completion_tokens": 816,
"completion_tokens_details": null,
"prompt_tokens": 102,
"prompt_tokens_details": null,
"total_tokens": 918
} |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: ⟨⟩]}])⟩]}\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- Do... | 5,794,254 | 405,794,254 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 7,
"full_sequence": "{[⟨([{[⟨⟩]}])⟩]}",
"generation_error": null,
"generation_failed": null,
"generation_trace... | dyck_language2 | {
"completion_tokens": 518,
"completion_tokens_details": null,
"prompt_tokens": 98,
"prompt_tokens_details": null,
"total_tokens": 616
} |
[
{
"content": "[DYCK LANGUAGE TASK]\n\nINPUT: ][]}}}}}}]]}]))])])}})\nDIRECTION: reverse (prepend opening brackets)\n\nCONSTRAINTS:\n- Minimize added brackets\n- Result must be valid Dyck word\n- Preserve input as suffix\n\nPlease provide your final answer in backticks like `answer`.",
"reasoning_content": n... | 156,921,733 | 556,921,733 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 20,
"full_sequence": "({{([([(([{[[{{{{{{[][]}}}}}}]]}]))])])}})",
"generation_error": null,
"generation_failed"... | dyck_language2 | {
"completion_tokens": 1336,
"completion_tokens_details": null,
"prompt_tokens": 75,
"prompt_tokens_details": null,
"total_tokens": 1411
} |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: )⟩)]⟨⟩{}()⟨⟩}{}}()\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid seque... | 191,230,895 | 591,230,895 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 6,
"full_sequence": "{{[(⟨()⟩)]⟨⟩{}()⟨⟩}{}}()",
"generation_error": null,
"generation_failed": null,
"generati... | dyck_language2 | {
"completion_tokens": 606,
"completion_tokens_details": null,
"prompt_tokens": 103,
"prompt_tokens_details": null,
"total_tokens": 709
} |
[
{
"content": "With numbers [4, 10, 14, 15] and operations ['+', '-', '*', '/'], get 72.\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there i... | 41,586,339 | 141,586,339 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 11212,
"completion_tokens_details": null,
"prompt_tokens": 95,
"prompt_tokens_details": null,
"total_tokens": 11307
} |
[
{
"content": "解决密码算术谜题：SSIIU + ISZMMM + SZZI = USMMMZ（其中SSIIU是5位数、ISZMMM是6位数、SZZI是4位数、USMMMZ是6位数），其中每个字母表示0-9之间的一个数字，不同字母代表不同数字。请计算出使等式成立的数字等式。 请在回答的最后一行使用以下格式：答案是 $YOUR_ANSWER。$YOUR_ANSWER 应该是替换为数字后的等式。",
"reasoning_content": null,
"role": "user"
},
{
"content": "答案是 88667 + 683000 + 8336 = 780... | 73,320,836 | 373,320,836 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": null,
"D": null,
"E": null,
"F": null,
"G": null,
"H": null,
"I": 6,
"J": null,
"K": null,
"L": null,
"M": 0,
"N": null,
"O": null,
"P": null,
... | cryptarithm | {
"completion_tokens": 6151,
"completion_tokens_details": null,
"prompt_tokens": 127,
"prompt_tokens_details": null,
"total_tokens": 6278
} |
[
{
"content": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: ())()]}]]()){}>}])<>][]<>[]<>[][]()[]<>()\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final a... | 70,294,500 | 470,294,500 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 11,
"full_sequence": "[([{<([[{[(())()]}]]()){}>}])<>][]<>[]<>[][]()[]<>()",
"generation_error": null,
"generati... | dyck_language2 | {
"completion_tokens": 1079,
"completion_tokens_details": null,
"prompt_tokens": 94,
"prompt_tokens_details": null,
"total_tokens": 1173
} |
[
{
"content": "Given [5, 5, 10, 13], compute 100 using ['+', '-', '*', '/'].\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there is no solutio... | 70,136,193 | 170,136,193 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 2487,
"completion_tokens_details": null,
"prompt_tokens": 93,
"prompt_tokens_details": null,
"total_tokens": 2580
} |
[
{
"content": "已知字母等式：JFKJ + JJ + KFKN - WK = FFJWK（其中JFKJ是4位数、JJ是2位数、KFKN是4位数、WK是2位数、FFJWK是5位数），每个字母代表一个数字，不同字母代表不同数字。请找出让等式成立的数字替换方案。 请在回答的最后一行使用以下格式：答案是 $YOUR_ANSWER。$YOUR_ANSWER 应该是替换为数字后的等式。",
"reasoning_content": null,
"role": "user"
},
{
"content": "已知字母等式：JFKJ + JJ + KFKN - WK = FFJWK，其中各... | 49,889,647 | 349,889,647 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": null,
"D": null,
"E": null,
"F": 1,
"G": null,
"H": null,
"I": null,
"J": 3,
"K": 8,
"L": null,
"M": null,
"N": 0,
"O": null,
"P": null,
"Q... | cryptarithm | {
"completion_tokens": 5687,
"completion_tokens_details": null,
"prompt_tokens": 123,
"prompt_tokens_details": null,
"total_tokens": 5810
} |
[
{
"content": "Fill in the blank:\n\n_____ + ()}})>⟩⟩]} = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
... | 467,789 | 400,467,789 | {
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"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 8,
"full_sequence": "{[⟨⟨<({{()}})>⟩⟩]}",
"generation_error": null,
"generation_failed": null,
"generation_tra... | dyck_language2 | {
"completion_tokens": 574,
"completion_tokens_details": null,
"prompt_tokens": 63,
"prompt_tokens_details": null,
"total_tokens": 637
} |
[
{
"content": "Consider the following logical expressions:\n\nA. The capital of Peru is New Delhi.\nB. The currency of Norway is the Franc.\nC. 1988 is a leap year.\nD. not not (((5 ** 3) == (-6 * 0 + 8 * -7)) or ((2 + 14) >= (3 ** 1)))\nE. not not (not not (55 is an even number.))\nF. ((Electricity flows faster... | 65,198,575 | 665,198,575 | {
"closing_sequence": null,
"depth": 2,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"The capital of Peru is New Delhi.",
"False"
],
[
"The currency of Norway is the Franc.",
"False"
],... | boolean_expressions | {
"completion_tokens": 402,
"completion_tokens_details": null,
"prompt_tokens": 160,
"prompt_tokens_details": null,
"total_tokens": 562
} |
[
{
"content": "Q: What opening brackets should precede \"()>)}[][]][][]{}<>[]\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`.... | 121,756,560 | 521,756,560 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 4,
"full_sequence": "[{(<()>)}[][]][][]{}<>[]",
"generation_error": null,
"generation_failed": null,
"generati... | dyck_language2 | {
"completion_tokens": 540,
"completion_tokens_details": null,
"prompt_tokens": 73,
"prompt_tokens_details": null,
"total_tokens": 613
} |
[
{
"content": "给定一个字母等式：IJ + NJ = MK，每个字母表示一个数字，不同字母表示不同数字。其中IJ是2位数，NJ是2位数，MK是2位数。请计算出满足条件的数字等式。 请在回答的最后一行使用以下格式：答案是 $YOUR_ANSWER。$YOUR_ANSWER 应该是替换为数字后的等式。",
"reasoning_content": null,
"role": "user"
},
{
"content": "根据字母等式 IJ + NJ = MK，每个字母代表一个数字，且不同字母表示不同数字。通过分析，满足条件的数字等式有多种可能。其中一种有效的解为：I=3, J... | 79,497,581 | 379,497,581 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": null,
"D": null,
"E": null,
"F": null,
"G": null,
"H": null,
"I": 3,
"J": 8,
"K": 6,
"L": null,
"M": 5,
"N": 1,
"O": null,
"P": null,
"Q": ... | cryptarithm | {
"completion_tokens": 4968,
"completion_tokens_details": null,
"prompt_tokens": 96,
"prompt_tokens_details": null,
"total_tokens": 5064
} |
[
{
"content": "You are an expert in Dyck language, where you must complete bracket sequences (e.g., [], {}, <>). You need to analyze whether the bracket matching steps are correct according to Dyck language rules.\n\nGiven an initial Dyck language sequence and steps for deriving the closing bracket sequence (giv... | 69,239,757 | 869,239,757 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "((([(()[()][])()][]))[])",
"error_indices": [
9,
11,
15
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_... | dyck_language_reasoning_errors | {
"completion_tokens": 379,
"completion_tokens_details": null,
"prompt_tokens": 499,
"prompt_tokens_details": null,
"total_tokens": 878
} |
[
{
"content": "Given the following boolean expressions:\n\nA. ((not (((-14 - 16) < (1 ** 1) < (8 + -15)) or (((23 % 4) <= (-15 * -18) <= (-4 + -1)) or (752 is a Fibonacci number.)))) or (((3 + 14) < (19 % 9)) and ((13 + -16) == (5 * 16)) and ((8 * -2 - -4 * -10) > (1 + -8)))) or ((not ((((-5 * -9 - -2 * 5) != (8... | 23,092,997 | 623,092,997 | {
"closing_sequence": null,
"depth": 5,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"((not (((-14 - 16) < (1 ** 1) < (8 + -15)) or (((23 % 4) <= (-15 * -18) <= (-4 + -1)) or (752 is a Fibonacci number.)))) or (((3 ... | boolean_expressions | {
"completion_tokens": 1565,
"completion_tokens_details": null,
"prompt_tokens": 692,
"prompt_tokens_details": null,
"total_tokens": 2257
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 13,862,641 | 813,862,641 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "()({})([[{}([])[]][]])({}())",
"error_indices": [
7,
8,
24,
25
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"... | dyck_language_reasoning_errors | {
"completion_tokens": 425,
"completion_tokens_details": null,
"prompt_tokens": 454,
"prompt_tokens_details": null,
"total_tokens": 879
} |
[
{
"content": "完成这道数独题目。将每个'.'替换为1到9之间的数字。\n\n```\n2.1.9.3..\n4.....17.\n....21..4\n62..5....\n31.24796.\n54...9..1\n.3..6.2..\n.8..7....\n764......\n```\n\n规则：每行、每列、每个3x3宫格都必须恰好包含数字1-9各一次。\n\n以相同格式输出解答，用三个反引号包裹。",
"reasoning_content": null,
"role": "user"
},
{
"content": "The completed Sudoku gr... | 95,588,128 | 795,588,128 | {
"closing_sequence": null,
"depth": null,
"difficulty": "medium",
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": ... | sudoku | {
"completion_tokens": 11320,
"completion_tokens_details": null,
"prompt_tokens": 128,
"prompt_tokens_details": null,
"total_tokens": 11448
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 26,673,815 | 826,673,815 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[]{}({[]}){}",
"error_indices": [
4,
6
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"gen... | dyck_language_reasoning_errors | {
"completion_tokens": 210,
"completion_tokens_details": null,
"prompt_tokens": 273,
"prompt_tokens_details": null,
"total_tokens": 483
} |
[
{
"content": "[DYCK LANGUAGE TASK]\n\nINPUT: ⟧⟩⟩]⟧]>\nDIRECTION: reverse (prepend opening brackets)\n\nCONSTRAINTS:\n- Minimize added brackets\n- Result must be valid Dyck word\n- Preserve input as suffix\n\nPlease provide your final answer in backticks like `answer`.",
"reasoning_content": null,
"role"... | 160,879,233 | 560,879,233 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 7,
"full_sequence": "<[⟦[⟨⟨⟦⟧⟩⟩]⟧]>",
"generation_error": null,
"generation_failed": null,
"generation_traceba... | dyck_language2 | {
"completion_tokens": 518,
"completion_tokens_details": null,
"prompt_tokens": 71,
"prompt_tokens_details": null,
"total_tokens": 589
} |
[
{
"content": "请解决以下数独谜题。用数字1-9填充空格（用'.'标记）。\n\n规则：\n- 每行必须包含数字1-9，不能重复\n- 每列必须包含数字1-9，不能重复\n- 每个3x3宫格必须包含数字1-9，不能重复\n\n谜题：\n```\n5..4....7\n.1....5.9\n4.9..71.3\n..4132..8\n.86..5...\n.7.98...4\n...82.9..\n.27.....6\n39....81.\n```\n\n请将完整的9x9网格（9行，每行9个数字）用三个反引号包裹后输出。",
"reasoning_content": null,
"role"... | 92,492,077 | 792,492,077 | {
"closing_sequence": null,
"depth": null,
"difficulty": "medium",
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": ... | sudoku | {
"completion_tokens": 11403,
"completion_tokens_details": null,
"prompt_tokens": 180,
"prompt_tokens_details": null,
"total_tokens": 11583
} |
[
{
"content": "Given the following boolean expressions:\n\nA. not not ((((-7 * -7 + -9 * 1) != (28 % 7)) and (The currency of Brazil is the Real.)) or (Canada is in North America.))\nB. ((not ((4 - -3) == (11 + -12))) and (((-9 + 0) > (8 + -2)) and (Copper is a liquid at room temperature.))) and (Oil is a liquid... | 13,205,638 | 613,205,638 | {
"closing_sequence": null,
"depth": 3,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"not not ((((-7 * -7 + -9 * 1) != (28 % 7)) and (The currency of Brazil is the Real.)) or (Canada is in North America.))",
"... | boolean_expressions | {
"completion_tokens": 710,
"completion_tokens_details": null,
"prompt_tokens": 308,
"prompt_tokens_details": null,
"total_tokens": 1018
} |
[
{
"content": "这里有一些需要评估的布尔表达式：\n\nA. 天王星是距离太阳第7近的行星。\nB. (金星是距离太阳第4近的行星。) and ((第一次世界大战结束发生在1916年。) or ((19 % 9) > (14 * -6)))\nC. (((26 % 9) > (-11 + 8)) or (金在常温下是固体。)) or ((火星是距离太阳第5近的行星。) and (水蒸气在常温下是液体。))\nD. 西班牙的首都是奥斯陆。\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。",
"reasoning_content": null,
"rol... | 21,662,793 | 621,662,793 | {
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"depth": 2,
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"digit_map": null,
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"expressions": [
[
"天王星是距离太阳第7近的行星。",
"True"
],
[
"(金星是距离太阳第4近的行星。) and ((第一次世界大战结束发生在1916年。) or ((19 % 9) > (14 * -6)))",
... | boolean_expressions | {
"completion_tokens": 362,
"completion_tokens_details": null,
"prompt_tokens": 167,
"prompt_tokens_details": null,
"total_tokens": 529
} |
[
{
"content": "下面是几个布尔表达式：\n\nA. (not ((not not ((((41 % 1) <= (-18 * -4)) or ((4 ** 2) <= (-18 + 16))) or (三月有31天。))) or (not ((42 % 4) > (-18 + -19))))) or (not (((not ((-1 * -10 + 2 * -10) == (1 * 4 * -2 * -7))) and ((not (铜在常温下是固体。)) or ((比利时的首都是惠灵顿。) or ((0 - 9) <= (8 - -8))))) or ((((金星是距离太阳第2近的行星。) and (十... | 46,973,494 | 646,973,494 | {
"closing_sequence": null,
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"digit_map": null,
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"expressions": [
[
"(not ((not not ((((41 % 1) <= (-18 * -4)) or ((4 ** 2) <= (-18 + 16))) or (三月有31天。))) or (not ((42 % 4) > (-18 + -19))))) or (not... | boolean_expressions | {
"completion_tokens": 3509,
"completion_tokens_details": null,
"prompt_tokens": 1480,
"prompt_tokens_details": null,
"total_tokens": 4989
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 7,909,033 | 807,909,033 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[]{}[][]([[(())[]]]())",
"error_indices": [
13,
18
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": ... | dyck_language_reasoning_errors | {
"completion_tokens": 326,
"completion_tokens_details": null,
"prompt_tokens": 390,
"prompt_tokens_details": null,
"total_tokens": 716
} |
[
{
"content": "Q: What opening brackets should precede \"⦃⦄⦄⦄}[]<>⟧⟦⟧⟦⟧<>⟧}>⟩}>⟩\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answe... | 102,775,820 | 502,775,820 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 11,
"full_sequence": "⟨<{⟨<{⟦⟦{⦃⦃⦃⦄⦄⦄}[]<>⟧⟦⟧⟦⟧<>⟧}>⟩}>⟩",
"generation_error": null,
"generation_failed": null,
... | dyck_language2 | {
"completion_tokens": 1008,
"completion_tokens_details": null,
"prompt_tokens": 88,
"prompt_tokens_details": null,
"total_tokens": 1096
} |
[
{
"content": "Q: What opening brackets should precede \"<>)[]>{}}()>⟩()⦃⦄}⦆⟧⦄⦆⦅⦆⦃⦄}()[]⟩⦄<>]⟨⟩<><>⦅⦆()\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) i... | 99,958,988 | 499,958,988 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 14,
"full_sequence": "[⦃⟨{⦅⦃⟦⦅{⟨<{<(<>)[]>{}}()>⟩()⦃⦄}⦆⟧⦄⦆⦅⦆⦃⦄}()[]⟩⦄<>]⟨⟩<><>⦅⦆()",
"generation_error": null,
"... | dyck_language2 | {
"completion_tokens": 1542,
"completion_tokens_details": null,
"prompt_tokens": 110,
"prompt_tokens_details": null,
"total_tokens": 1652
} |
[
{
"content": "A sequence of brackets was cut, and only the end remains:\n\n\"){}}()\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored complete sequence) ... | 70,874,656 | 470,874,656 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 2,
"full_sequence": "{(){}}()",
"generation_error": null,
"generation_failed": null,
"generation_traceback": n... | dyck_language2 | {
"completion_tokens": 294,
"completion_tokens_details": null,
"prompt_tokens": 75,
"prompt_tokens_details": null,
"total_tokens": 369
} |
[
{
"content": "Define ☆, the rules are as follows:\nwhen the sum of x and y is odd, x ☆ y = y / x;\notherwise, x ☆ y = x ** y.\nand ⊕, the rules are as follows:\nwhen the sum of x and y is odd, x ⊕ y = x + y / y;\notherwise, x ⊕ y = x - y ☆ x.\nThe precedence of operations: ☆ > ** > * = / = % = ⊕ > + = -... | 99,450,234 | 299,450,234 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "4 ⊕ 10",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": ... | operation | {
"completion_tokens": 421,
"completion_tokens_details": null,
"prompt_tokens": 159,
"prompt_tokens_details": null,
"total_tokens": 580
} |
[
{
"content": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: {}⟦⟧⟧}⟩⟩})>)>}>\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nP... | 22,979,559 | 422,979,559 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 11,
"full_sequence": "<{<(<({⟨⟨{⟦{}⟦⟧⟧}⟩⟩})>)>}>",
"generation_error": null,
"generation_failed": null,
"gener... | dyck_language2 | {
"completion_tokens": 797,
"completion_tokens_details": null,
"prompt_tokens": 91,
"prompt_tokens_details": null,
"total_tokens": 888
} |
[
{
"content": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: >)>)]]⟩⦄>⟩⟧]⟩⟩⟧]]⟩}⟩)}]⟧⟩⦄⟩\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the ful... | 39,144,816 | 439,144,816 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 27,
"full_sequence": "⟨⦃⟨⟦[{(⟨{⟨[[⟦⟨⟨[⟦⟨<⦃⟨[[(<(<>)>)]]⟩⦄>⟩⟧]⟩⟩⟧]]⟩}⟩)}]⟧⟩⦄⟩",
"generation_error": null,
"genera... | dyck_language2 | {
"completion_tokens": 2201,
"completion_tokens_details": null,
"prompt_tokens": 102,
"prompt_tokens_details": null,
"total_tokens": 2303
} |
[
{
"content": "Use [7, 11, 11, 16, 18] with ['+', '-', '*', '/'] to get 36.\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there is no solution... | 98,798,625 | 198,798,625 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
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"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 2054,
"completion_tokens_details": null,
"prompt_tokens": 98,
"prompt_tokens_details": null,
"total_tokens": 2152
} |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: }⟩[])}\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- Do no... | 151,411,858 | 551,411,858 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 4,
"full_sequence": "{(⟨{}⟩[])}",
"generation_error": null,
"generation_failed": null,
"generation_traceback":... | dyck_language2 | {
"completion_tokens": 365,
"completion_tokens_details": null,
"prompt_tokens": 95,
"prompt_tokens_details": null,
"total_tokens": 460
} |
[
{
"content": "A sequence of brackets was cut, and only the end remains:\n\n\"){})()())\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored complete sequenc... | 80,466,612 | 480,466,612 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 3,
"full_sequence": "(((){})()())",
"generation_error": null,
"generation_failed": null,
"generation_traceback... | dyck_language2 | {
"completion_tokens": 357,
"completion_tokens_details": null,
"prompt_tokens": 76,
"prompt_tokens_details": null,
"total_tokens": 433
} |
[
{
"content": "Define ◎, the rules are as follows:\nwhen x is a multiple of 3, x ◎ y = y - x - 4 - x;\notherwise, x ◎ y = (2 + x) + x + y.\nand □, the rules are as follows:\nwhen x and y are both odd, x □ y = x - x + x * y;\notherwise, x □ y = y ◎ x + x * x.\nThe precedence of operations: □ > ◎ > ** > * ... | 73,746,450 | 273,746,450 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "4 * 8 □ 10 ◎ 9",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_trac... | operation | {
"completion_tokens": 562,
"completion_tokens_details": null,
"prompt_tokens": 183,
"prompt_tokens_details": null,
"total_tokens": 745
} |
[
{
"content": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: ()<>⟧>]⟩⟩⟧}}]}⟩>>]⟧⟩>\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full bala... | 115,076,753 | 515,076,753 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 17,
"full_sequence": "<⟨⟦[<<⟨{[{{⟦⟨⟨[<⟦()<>⟧>]⟩⟩⟧}}]}⟩>>]⟧⟩>",
"generation_error": null,
"generation_failed": nu... | dyck_language2 | {
"completion_tokens": 1249,
"completion_tokens_details": null,
"prompt_tokens": 91,
"prompt_tokens_details": null,
"total_tokens": 1340
} |
[
{
"content": "A sequence of brackets was cut, and only the end remains:\n\n\"⟩]]))]]>})⟩>])>]}⟩}\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored comple... | 198,695,565 | 598,695,565 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 19,
"full_sequence": "{⟨{[<([<⟨({<[[(([[⟨⟩]]))]]>})⟩>])>]}⟩}",
"generation_error": null,
"generation_failed": nu... | dyck_language2 | {
"completion_tokens": 1276,
"completion_tokens_details": null,
"prompt_tokens": 85,
"prompt_tokens_details": null,
"total_tokens": 1361
} |
[
{
"content": "[DYCK LANGUAGE TASK]\n\nINPUT: )[][]]}})>⟦⟧⟩{}<>)]}{}⟩{}⟨⟩⟨⟩>⟦⟧\nDIRECTION: reverse (prepend opening brackets)\n\nCONSTRAINTS:\n- Minimize added brackets\n- Result must be valid Dyck word\n- Preserve input as suffix\n\nPlease provide your final answer in backticks like `answer`.",
"reasoning_c... | 54,460,405 | 454,460,405 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 12,
"full_sequence": "<⟨{[(⟨<({{[()[][]]}})>⟦⟧⟩{}<>)]}{}⟩{}⟨⟩⟨⟩>⟦⟧",
"generation_error": null,
"generation_faile... | dyck_language2 | {
"completion_tokens": 1080,
"completion_tokens_details": null,
"prompt_tokens": 87,
"prompt_tokens_details": null,
"total_tokens": 1167
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 72,048,840 | 872,048,840 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "(()){}({})()",
"error_indices": [
11,
12
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"g... | dyck_language_reasoning_errors | {
"completion_tokens": 218,
"completion_tokens_details": null,
"prompt_tokens": 274,
"prompt_tokens_details": null,
"total_tokens": 492
} |
[
{
"content": "定义 ◇，规则如下：\n当x和y都是奇数时，x ◇ y = y - (x - x)；\n其他情况下，x ◇ y = x - x + y。\n运算优先级：** = ◇ > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 1 % 2 + 8 ◇ 4\n请将最终答案填入\\boxed{}中。",
"reasoning_content": null,
"role": "user"
},
{
"content": "根据给定的运算符定义，当 \\(x\\) 和 \\(y\\) 都是奇数时，\\(x \\... | 76,691,591 | 276,691,591 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "1 % 2 + 8 ◇ 4",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_trace... | operation | {
"completion_tokens": 1062,
"completion_tokens_details": null,
"prompt_tokens": 119,
"prompt_tokens_details": null,
"total_tokens": 1181
} |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: ))]]}()]}()[]]}){})[]){}()){}()()()[][]{}{}\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepen... | 27,267,908 | 427,267,908 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 13,
"full_sequence": "(((({[{[{[[(())]]}()]}()[]]}){})[]){}()){}()()()[][]{}{}",
"generation_error": null,
"gene... | dyck_language2 | {
"completion_tokens": 1205,
"completion_tokens_details": null,
"prompt_tokens": 112,
"prompt_tokens_details": null,
"total_tokens": 1317
} |
[
{
"content": "Let S = \"){}⟨⟩\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
{
"content": "`(){}⟨⟩`"... | 39,853,453 | 439,853,453 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 1,
"full_sequence": "(){}⟨⟩",
"generation_error": null,
"generation_failed": null,
"generation_traceback": nul... | dyck_language2 | {
"completion_tokens": 267,
"completion_tokens_details": null,
"prompt_tokens": 68,
"prompt_tokens_details": null,
"total_tokens": 335
} |
[
{
"content": "Let S = \">>}[]]>}⟨⟩<>⟨⟩]⟩(){})))⟩⟩]}⟩}\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
{
... | 51,761,357 | 451,761,357 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 17,
"full_sequence": "{⟨{[⟨⟨(((⟨[{<[{<<>>}[]]>}⟨⟩<>⟨⟩]⟩(){})))⟩⟩]}⟩}",
"generation_error": null,
"generation_fai... | dyck_language2 | {
"completion_tokens": 1322,
"completion_tokens_details": null,
"prompt_tokens": 83,
"prompt_tokens_details": null,
"total_tokens": 1405
} |
[
{
"content": "考虑以下布尔表达式：\n\nA. ((not (((9 * 2 - 6 * 3) >= (15 - -16)) and (十月有29天。))) and (((印度位于南极洲。) and ((-1 * 1) <= (2 ** 1))) and (((20 - -5) != (-4 * 8 + -8 * 6)) and (马有4条腿。)))) or (not not (not not (2000年奥运会在东京举办。))) or ((not (((-5 - 14) <= (-1 * 8 - -9 * 7)) or ((9 * 12) != (-8 - -2)))) and (((-18 * 14... | 16,941,932 | 616,941,932 | {
"closing_sequence": null,
"depth": 4,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"((not (((9 * 2 - 6 * 3) >= (15 - -16)) and (十月有29天。))) and (((印度位于南极洲。) and ((-1 * 1) <= (2 ** 1))) and (((20 - -5) != (-4 * 8 + ... | boolean_expressions | {
"completion_tokens": 1657,
"completion_tokens_details": null,
"prompt_tokens": 704,
"prompt_tokens_details": null,
"total_tokens": 2361
} |
[
{
"content": "Fill in the blank:\n\n_____ + >>⟧()<>{}>]<>()<>⟦⟧}>())⟧⟨⟩>]]}>>⟧>}> = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`.",
"reasoning_content": null... | 15,037,251 | 415,037,251 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 19,
"full_sequence": "<{<⟦<<{[[<⟦(<{[<⟦<<>>⟧()<>{}>]<>()<>⟦⟧}>())⟧⟨⟩>]]}>>⟧>}>",
"generation_error": null,
"gene... | dyck_language2 | {
"completion_tokens": 1555,
"completion_tokens_details": null,
"prompt_tokens": 80,
"prompt_tokens_details": null,
"total_tokens": 1635
} |
[
{
"content": "下面是几个布尔表达式：\n\nA. 1956年是闰年。\nB. ((707是斐波那契数。) or (161是斐波那契数。)) and (not ((-5 * 6 - 5 * 10) > (5 ** 1)))\nC. not not (电流比光速更快。)\nD. ((水星是距离太阳第1近的行星。) or ((-1 * 0 * 1 * 6) < (33 % 10))) or (氮气在常温下是气体。)\nE. not ((闪电不会两次击中同一个地方。) and (印度尼西亚的首都是雅加达。))\nF. 二月有28天。\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。... | 43,705,608 | 643,705,608 | {
"closing_sequence": null,
"depth": 2,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"1956年是闰年。",
"True"
],
[
"((707是斐波那契数。) or (161是斐波那契数。)) and (not ((-5 * 6 - 5 * 10) > (5 ** 1)))",
"Fal... | boolean_expressions | {
"completion_tokens": 486,
"completion_tokens_details": null,
"prompt_tokens": 198,
"prompt_tokens_details": null,
"total_tokens": 684
} |
[
{
"content": "Let S = \"})[]}]]}]]{})()[][]\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
{
"conten... | 42,302,186 | 442,302,186 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 9,
"full_sequence": "([[{[[{({})[]}]]}]]{})()[][]",
"generation_error": null,
"generation_failed": null,
"gene... | dyck_language2 | {
"completion_tokens": 712,
"completion_tokens_details": null,
"prompt_tokens": 72,
"prompt_tokens_details": null,
"total_tokens": 784
} |
[
{
"content": "Define ⊗, the rules are as follows:\non the real number field, x ⊗ y = y * x - y.\nand ⊙, the rules are as follows:\non the real number field, x ⊙ y = y + x ⊗ y.\nand ♢, the rules are as follows:\nwhen x is equal to y, x ♢ y = y + x ⊗ y;\notherwise, x ♢ y = y + y + (x).\nThe precedence of ... | 59,925,290 | 259,925,290 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "6 * 3 ⊗ 7 ♢ 9 ⊙ 6",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_t... | operation | {
"completion_tokens": 904,
"completion_tokens_details": null,
"prompt_tokens": 190,
"prompt_tokens_details": null,
"total_tokens": 1094
} |
[
{
"content": "Using [6, 6, 7, 8], calculate 36 with ['+', '-'].\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there is no solution, please ou... | 90,917,742 | 190,917,742 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 2639,
"completion_tokens_details": null,
"prompt_tokens": 88,
"prompt_tokens_details": null,
"total_tokens": 2727
} |
[
{
"content": "You are an expert in Dyck language, where you must complete bracket sequences (e.g., [], {}, <>). You need to analyze whether the bracket matching steps are correct according to Dyck language rules.\n\nGiven an initial Dyck language sequence and steps for deriving the closing bracket sequence (giv... | 89,284,517 | 889,284,517 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "()<[]()>()",
"error_indices": [
4,
8
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"gener... | dyck_language_reasoning_errors | {
"completion_tokens": 188,
"completion_tokens_details": null,
"prompt_tokens": 328,
"prompt_tokens_details": null,
"total_tokens": 516
} |
[
{
"content": "有一个等式：VA + AF = VDQ，其中每个字母代表一个不同的数字（VA 是 2 位数、AF 是 2 位数、VDQ 是 3 位数）。请找出每个字母代表的数字，使等式成立。 请在回答的最后一行使用以下格式：答案是 $YOUR_ANSWER。$YOUR_ANSWER 应该是替换为数字后的等式。",
"reasoning_content": null,
"role": "user"
},
{
"content": "根据题目要求，等式为 VA + AF = VDQ，其中 VA 和 AF 是两位数，VDQ 是三位数，且每个字母代表不同的数字。\n\n---\n\... | 42,665,667 | 342,665,667 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": 8,
"B": null,
"C": null,
"D": 0,
"E": null,
"F": 6,
"G": null,
"H": null,
"I": null,
"J": null,
"K": null,
"L": null,
"M": null,
"N": null,
"O": null,
"P": null,
... | cryptarithm | {
"completion_tokens": 9073,
"completion_tokens_details": null,
"prompt_tokens": 100,
"prompt_tokens_details": null,
"total_tokens": 9173
} |
[
{
"content": "Fill in the blank:\n\n_____ + <>)] = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
{
... | 166,432,944 | 566,432,944 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 2,
"full_sequence": "[(<>)]",
"generation_error": null,
"generation_failed": null,
"generation_traceback": nul... | dyck_language2 | {
"completion_tokens": 268,
"completion_tokens_details": null,
"prompt_tokens": 59,
"prompt_tokens_details": null,
"total_tokens": 327
} |
[
{
"content": "Using [5, 7, 10, 13], apply the operations ['+', '-', '*'] to calculate 24.\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there... | 64,215,249 | 164,215,249 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 1961,
"completion_tokens_details": null,
"prompt_tokens": 94,
"prompt_tokens_details": null,
"total_tokens": 2055
} |
[
{
"content": "Numbers [5, 8, 8, 9, 9], find 60 using ['+', '-'].\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there is no solution, please o... | 59,052,686 | 159,052,686 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 3126,
"completion_tokens_details": null,
"prompt_tokens": 91,
"prompt_tokens_details": null,
"total_tokens": 3217
} |
[
{
"content": "Q: What opening brackets should precede \"}⟩>⦄][]}[]⟩⦄⟦⟧()⟨⟩{}\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`.... | 173,333,585 | 573,333,585 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 8,
"full_sequence": "⦃⟨{[⦃<⟨{}⟩>⦄][]}[]⟩⦄⟦⟧()⟨⟩{}",
"generation_error": null,
"generation_failed": null,
"gene... | dyck_language2 | {
"completion_tokens": 780,
"completion_tokens_details": null,
"prompt_tokens": 82,
"prompt_tokens_details": null,
"total_tokens": 862
} |
[
{
"content": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: <>()]>)]⟩)⟩}[]()<>⟨⟩()<>()<>()<>[]\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (... | 168,388,992 | 568,388,992 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 8,
"full_sequence": "{⟨(⟨[(<[<>()]>)]⟩)⟩}[]()<>⟨⟩()<>()<>()<>[]",
"generation_error": null,
"generation_failed":... | dyck_language2 | {
"completion_tokens": 904,
"completion_tokens_details": null,
"prompt_tokens": 96,
"prompt_tokens_details": null,
"total_tokens": 1000
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 63,160,646 | 863,160,646 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "{}[]{([]()()({}()))}()",
"error_indices": [
8,
13
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": n... | dyck_language_reasoning_errors | {
"completion_tokens": 328,
"completion_tokens_details": null,
"prompt_tokens": 392,
"prompt_tokens_details": null,
"total_tokens": 720
} |
[
{
"content": "已知字母等式：ASBA - AACSBC + BBSBCB = ASBBCS（其中ASBA是4位数、AACSBC是6位数、BBSBCB是6位数、ASBBCS是6位数），每个字母代表一个数字，不同字母代表不同数字。请找出让等式成立的数字替换方案。 请在回答的最后一行使用以下格式：答案是 $YOUR_ANSWER。$YOUR_ANSWER 应该是替换为数字后的等式。",
"reasoning_content": null,
"role": "user"
},
{
"content": "已知字母等式： \n**ASBA - AACSBC + BBSBCB = ... | 32,848,768 | 332,848,768 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": 4,
"B": 8,
"C": 9,
"D": null,
"E": null,
"F": null,
"G": null,
"H": null,
"I": null,
"J": null,
"K": null,
"L": null,
"M": null,
"N": null,
"O": null,
"P": null,
... | cryptarithm | {
"completion_tokens": 9047,
"completion_tokens_details": null,
"prompt_tokens": 120,
"prompt_tokens_details": null,
"total_tokens": 9167
} |
[
{
"content": "Fill in the blank:\n\n_____ + ⟧>)⟧⟩]>>⟩}> = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
... | 7,005,444 | 407,005,444 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 11,
"full_sequence": "<{⟨<<[⟨⟦(<⟦⟧>)⟧⟩]>>⟩}>",
"generation_error": null,
"generation_failed": null,
"generatio... | dyck_language2 | {
"completion_tokens": 739,
"completion_tokens_details": null,
"prompt_tokens": 66,
"prompt_tokens_details": null,
"total_tokens": 805
} |
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