env stringclasses 1
value | prompt stringlengths 203 478 | extra dict |
|---|---|---|
logic-v2 | Let S = "])}]}]]))])}]]]]}]]})" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "({[[{[[[[{([(([[{[{([])}]}]]))])}]]]]}]]})",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 21,
"full_sequence": "({[[{[[[[{([(([[{[{([])}]}]]))])}]]]]}]]})",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({[[{[[[[{([(... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: )}>>>>]]]
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[[[<<<<{()}>>>>]]]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "[[[<<<<{()}>>>>]]]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[[[<<<<{(",
"prompt_name": "puzzle",
"prompt_varia... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: ⟧⟧)⟦⟧})⟨⟩}>{}⟨⟩)⟧>>>
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final a... | {
"game_data": {
"answer": "<<<⟦(<{({(⟦⟦⟧⟧)⟦⟧})⟨⟩}>{}⟨⟩)⟧>>>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "<<<⟦(<{({(⟦⟦⟧⟧)⟦⟧})⟨⟩}>{}⟨⟩)⟧>>>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<<⟦(<{({(⟦⟦",
"prompt_name... |
logic-v2 | Let S = ")<>]⟧}))⟩⦆]⦄>>)⟧⦄" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "⦃⟦(<<⦃[⦅⟨(({⟦[()<>]⟧}))⟩⦆]⦄>>)⟧⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 15,
"full_sequence": "⦃⟦(<<⦃[⦅⟨(({⟦[()<>]⟧}))⟩⦆]⦄>>)⟧⦄",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦃⟦(<<⦃[⦅⟨(({⟦[(",
"prompt_n... |
logic-v2 | Q: What opening brackets should precede "⟧⟩>⟧]>}]⟩⟩⦄⟧⟧⟩>]⟩⟩)>>⦄⟧⟩" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨⟦⦃<<(⟨⟨[<⟨⟦⟦⦃⟨⟨[{<[⟦<⟨⟦⟧⟩>⟧]>}]⟩⟩⦄⟧⟧⟩>]⟩⟩)>>⦄⟧⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 24,
"full_sequence": "⟨⟦⦃<<(⟨⟨[<⟨⟦⟦⦃⟨⟨[{<[⟦<⟨⟦⟧⟩>⟧]>}]⟩⟩⦄⟧⟧⟩>]⟩⟩)>>⦄⟧⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: ]()⟩)⦄⟩})⟩]⦆⟩
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (... | {
"game_data": {
"answer": "⟨⦅[⟨({⟨⦃(⟨[]()⟩)⦄⟩})⟩]⦆⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "⟨⦅[⟨({⟨⦃(⟨[]()⟩)⦄⟩})⟩]⦆⟩",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟨⦅[⟨({⟨⦃(⟨[",
"prompt_name": "reverse_persp... |
logic-v2 | Q: What opening brackets should precede "()()}}][]}]][][]{}}}]()[]}])})()(){}{}" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "({([{[{{[[{[{{()()}}][]}]][][]{}}}]()[]}])})()(){}{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 14,
"full_sequence": "({([{[{{[[{[{{()()}}][]}]][][]{}}}]()[]}])})()(){}{}",
"n_types": 3,
"nesting_depth": 0,
"opening_pre... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ⦄)⟧)<>⟧]⟦⟧<>}⟩{}⟦⟧
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra b... | {
"game_data": {
"answer": "⟨{[⟦(⟦(⦃⦄)⟧)<>⟧]⟦⟧<>}⟩{}⟦⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 8,
"full_sequence": "⟨{[⟦(⟦(⦃⦄)⟧)<>⟧]⟦⟧<>}⟩{}⟦⟧",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨{[⟦(⟦(⦃",
"prompt_name": "direct",
... |
logic-v2 | Q: What opening brackets should precede ">]}]))>]>)])>>]" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[<<([(<[<(([{[<>]}]))>]>)])>>]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 15,
"full_sequence": "[<<([(<[<(([{[<>]}]))>]>)])>>]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<<([(<[<(([{[<",
"prompt_name"... |
logic-v2 | Let S = "{}]⦅⦆⦄⟦⟧}}⦃⦄⟩)⦅⦆[])⟩⟩[]⟧{})⦃⦄[][](){}[]" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "(⟦⟨⟨((⟨{{⦃[{}]⦅⦆⦄⟦⟧}}⦃⦄⟩)⦅⦆[])⟩⟩[]⟧{})⦃⦄[][](){}[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "(⟦⟨⟨((⟨{{⦃[{}]⦅⦆⦄⟦⟧}}⦃⦄⟩)⦅⦆[])⟩⟩[]⟧{})⦃⦄[][](){}[]",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix"... |
logic-v2 | Let S = "⟩⟩[]}⟩[]}>⟧{}⟧⟧}>" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "<{⟦⟦⟦<{⟨{⟨⟨⟩⟩[]}⟩[]}>⟧{}⟧⟧}>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "<{⟦⟦⟦<{⟨{⟨⟨⟩⟩[]}⟩[]}>⟧{}⟧⟧}>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{⟦⟦⟦<{⟨{⟨⟨",
"prompt_name": "mathe... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ⟩⟨⟩]⟩⟦⟧[]⟧⟩>⦄⟧}⟩})⦃⦄{}>⟧]()]⦃⦄⦄⦃⦄⟩⟦⟧[]⟨⟩
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "⟨⦃[[⟦<({⟨{⟦⦃<⟨⟦⟨[⟨⟩⟨⟩]⟩⟦⟧[]⟧⟩>⦄⟧}⟩})⦃⦄{}>⟧]()]⦃⦄⦄⦃⦄⟩⟦⟧[]⟨⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 18,
"full_sequence": "⟨⦃[[⟦<({⟨{⟦⦃<⟨⟦⟨[⟨⟩⟨⟩]⟩⟦⟧[]⟧⟩>⦄⟧}⟩})⦃⦄{}>⟧]()]⦃⦄⦄⦃⦄⟩⟦⟧[]⟨⟩",
"n_types": 7,
"nesting_depth": 0,
... |
logic-v2 | Q: What opening brackets should precede "]>⟨⟩()<>{}()" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<[]>⟨⟩()<>{}()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 2,
"full_sequence": "<[]>⟨⟩()<>{}()",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<[",
"prompt_name": "qa",
"prompt_variant": 6,
"seed... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: <>()()<>)}])}>>}()(){}>>]>)))⟩⟩>}]}}
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) i... | {
"game_data": {
"answer": "{{[{<⟨⟨(((<[<<{<<{([{(<>()()<>)}])}>>}()(){}>>]>)))⟩⟩>}]}}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 22,
"full_sequence": "{{[{<⟨⟨(((<[<<{<<{([{(<>()()<>)}])}>>}()(){}>>]>)))⟩⟩>}]}}",
"n_types": 5,
"nesting_depth": 0,
... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: []]()}]]]][]}{}){}>}}]})>})]
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add a... | {
"game_data": {
"answer": "[({<({[{{<({[[[[{[[]]()}]]]][]}{}){}>}}]})>})]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 18,
"full_sequence": "[({<({[{{<({[[[[{[[]]()}]]]][]}{}){}>}}]})>})]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[({<(... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: )⦄)<>{}>⟦⟧<>⟧⟧[]{}}><>⟧⟦⟧)}⟧⟩⟨⟩⟨⟩
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not ... | {
"game_data": {
"answer": "⟨⟦{(⟦<{⟦⟦<(⦃()⦄)<>{}>⟦⟧<>⟧⟧[]{}}><>⟧⟦⟧)}⟧⟩⟨⟩⟨⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "⟨⟦{(⟦<{⟦⟦<(⦃()⦄)<>{}>⟦⟧<>⟧⟧[]{}}><>⟧⟦⟧)}⟧⟩⟨⟩⟨⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟦{(⟦... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"()()[]]{}]])])]]])"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `an... | {
"game_data": {
"answer": "([[[([([[[()()[]]{}]])])]]])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "([[[([([[[()()[]]{}]])])]]])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([[[([([[[",
"prompt_name": "story"... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"}⟩⟦⟧[])}>}⟩<>}>}>"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `ans... | {
"game_data": {
"answer": "<{<{⟨{<{(⟨{}⟩⟦⟧[])}>}⟩<>}>}>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "<{<{⟨{<{(⟨{}⟩⟦⟧[])}>}⟩<>}>}>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{<{⟨{<{(⟨{",
"prompt_name": "story... |
logic-v2 | Q: What opening brackets should precede "><>()⟩⟩>]()<>}}" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{{[<⟨⟨<><>()⟩⟩>]()<>}}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 7,
"full_sequence": "{{[<⟨⟨<><>()⟩⟩>]()<>}}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{{[<⟨⟨<",
"prompt_name": "qa",
"prompt_var... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"]⟧⟨⟩()⦄⦆⟧⟧⟩⟧}⟧}>>⟩]⟩⦆)⟩)⟧}⟩⦆"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backtick... | {
"game_data": {
"answer": "⦅⟨{⟦(⟨(⦅⟨[⟨<<{⟦{⟦⟨⟦⟦⦅⦃⟦[]⟧⟨⟩()⦄⦆⟧⟧⟩⟧}⟧}>>⟩]⟩⦆)⟩)⟧}⟩⦆",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 24,
"full_sequence": "⦅⟨{⟦(⟨(⦅⟨[⟨<<{⟦{⟦⟨⟦⟦⦅⦃⟦[]⟧⟨⟩()⦄⦆⟧⟧⟩⟧}⟧}>>⟩]⟩⦆)⟩)⟧}⟩⦆",
"n_types": 8,
"nesting_depth": 0,
"opening_pre... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ⟩)()]⟩⟩>>}{}]⟨⟩]{}{}[][]{}⟨⟩⟨⟩⟩⟩{}}
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "{⟨⟨[[{<<⟨⟨[(⟨⟩)()]⟩⟩>>}{}]⟨⟩]{}{}[][]{}⟨⟩⟨⟩⟩⟩{}}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "{⟨⟨[[{<<⟨⟨[(⟨⟩)()]⟩⟩>>}{}]⟨⟩]{}{}[][]{}⟨⟩⟨⟩⟩⟩{}}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"){}()[]))"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "(((){}()[]))",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 3,
"full_sequence": "(((){}()[]))",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(((",
"prompt_name": "story",
"prompt_variant": 4,
"seed... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: }}})]}}<>()()[]<>
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answ... | {
"game_data": {
"answer": "{{[({{{}}})]}}<>()()[]<>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 7,
"full_sequence": "{{[({{{}}})]}}<>()()[]<>",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{{[({{{",
"prompt_name": "reverse_perspectiv... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: >}>>⟩)>]>}}
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`... | {
"game_data": {
"answer": "{{<[<(⟨<<{<>}>>⟩)>]>}}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "{{<[<(⟨<<{<>}>>⟩)>]>}}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{{<[<(⟨<<{<",
"prompt_name": "puzzle",
"p... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: >()⟩>⟧))[])]}>()⟩⟦⟧
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "⟨<{[(((⟦<⟨<>()⟩>⟧))[])]}>()⟩⟦⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "⟨<{[(((⟦<⟨<>()⟩>⟧))[])]}>()⟩⟦⟧",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨<{[(((⟦<⟨<",
"prompt_name": "t... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"⦅⦆}<>)"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "({⦅⦆}<>)",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 2,
"full_sequence": "({⦅⦆}<>)",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "({",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 910945... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"]⟩⟩}⟧]>"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<[⟦{⟨⟨[]⟩⟩}⟧]>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 7,
"full_sequence": "<[⟦{⟨⟨[]⟩⟩}⟧]>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<[⟦{⟨⟨[",
"prompt_name": "story",
"prompt_variant": 4,
... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"⟩<>)}⟧⦆()⦄⦆⦅⦆⦄>⦃⦄⦆⟩])⦆)⟨⟩{}<>⟩>⟦⟧{}⦃⦄[]"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) ... | {
"game_data": {
"answer": "<⟨(⦅([⟨⦅<⦃⦅⦃⦅⟦{(⟨⟩<>)}⟧⦆()⦄⦆⦅⦆⦄>⦃⦄⦆⟩])⦆)⟨⟩{}<>⟩>⟦⟧{}⦃⦄[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"full_sequence": "<⟨(⦅([⟨⦅<⦃⦅⦃⦅⟦{(⟨⟩<>)}⟧⦆()⦄⦆⦅⦆⦄>⦃⦄⦆⟩])⦆)⟨⟩{}<>⟩>⟦⟧{}⦃⦄[]",
"n_types": 8,
"nesting_depth": 0,
"ope... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: )][]{}
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "[()][]{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 2,
"full_sequence": "[()][]{}",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[(",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 54... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ])}⟨⟩[]()
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "{([])}⟨⟩[]()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 3,
"full_sequence": "{([])}⟨⟩[]()",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{([",
"prompt_name": "technical",
"prompt_variant": 3,
"... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"<>()}()}]]"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[[{{<>()}()}]]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 4,
"full_sequence": "[[{{<>()}()}]]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[[{{",
"prompt_name": "story",
"prompt_variant": 4,
... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
">]}[][]}{}>}>}>}]"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `ans... | {
"game_data": {
"answer": "[{<{<{<{{[<>]}[][]}{}>}>}>}]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "[{<{<{<{{[<>]}[][]}{}>}>}>}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{<{<{<{{[<",
"prompt_name": "story... |
logic-v2 | Fill in the blank:
_____ + ]}()())>>]}]{})[][]>}()][]<>{} = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[{<([{[<<({[]}()())>>]}]{})[][]>}()][]<>{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "[{<([{[<<({[]}()())>>]}]{})[][]>}()][]<>{}",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{<([{[<<({["... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ()[]][])][][]]}{})()}}]}[][]))})[][][]
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do... | {
"game_data": {
"answer": "({(({[{{({[[([()[]][])][][]]}{})()}}]}[][]))})[][][]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 14,
"full_sequence": "({(({[{{({[[([()[]][])][][]]}{})()}}]}[][]))})[][][]",
"n_types": 3,
"nesting_depth": 0,
"opening_pre... |
logic-v2 | Fill in the blank:
_____ + ⦃⦄⟦⟧⟦⟧⟩>⦆]⟩⦆⟩⟩ = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨⟨⦅⟨[⦅<⟨⦃⦄⟦⟧⟦⟧⟩>⦆]⟩⦆⟩⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 8,
"full_sequence": "⟨⟨⦅⟨[⦅<⟨⦃⦄⟦⟧⟦⟧⟩>⦆]⟩⦆⟩⟩",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟨⟨⦅⟨[⦅<⟨",
"prompt_name": "fill_in",
"prom... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ){}]⟨⟩)[]⟧⟩>}>⟩]⟧}⟩}⟩)⟩})⟩>>]⟧]>>
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in b... | {
"game_data": {
"answer": "<<[⟦[<<⟨({⟨(⟨{⟨{⟦[⟨<{<⟨⟦([(){}]⟨⟩)[]⟧⟩>}>⟩]⟧}⟩}⟩)⟩})⟩>>]⟧]>>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 27,
"full_sequence": "<<[⟦[<<⟨({⟨(⟨{⟨{⟦[⟨<{<⟨⟦([(){}]⟨⟩)[]⟧⟩>}>⟩]⟧}⟩}⟩)⟩})⟩>>]⟧]>>",
"n_types": 6,
"nesting_depth": 0,
... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: >>}>]>{}}>}]())))>>>)>)])>]
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add an... | {
"game_data": {
"answer": "[<([(<(<<<((([{<{<[<{<<>>}>]>{}}>}]())))>>>)>)])>]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 23,
"full_sequence": "[<([(<(<<<((([{<{<[<{<<>>}>]>{}}>}]())))>>>)>)])>]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix"... |
logic-v2 | Let S = "⟦⟧⟧⟩)" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "(⟨⟦⟦⟧⟧⟩)",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 3,
"full_sequence": "(⟨⟦⟦⟧⟧⟩)",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "(⟨⟦",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed"... |
logic-v2 | Let S = "]{}()⟨⟩<>}⦄[]<>⟩⦄⦄⟩<>⟧⦃⦄]⟩⟩⟧⟧⟩⦄⟧⟩" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "⟨⟦⦃⟨⟦⟦⟨⟨[⟦⟨⦃⦃⟨⦃{[]{}()⟨⟩<>}⦄[]<>⟩⦄⦄⟩<>⟧⦃⦄]⟩⟩⟧⟧⟩⦄⟧⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"full_sequence": "⟨⟦⦃⟨⟦⟦⟨⟨[⟦⟨⦃⦃⟨⦃{[]{}()⟨⟩<>}⦄[]<>⟩⦄⦄⟩<>⟧⦃⦄]⟩⟩⟧⟧⟩⦄⟧⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix"... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: {}()⟧⟩]⟦⟧⟨⟩[]⟦⟧}()>[]})⟧⟩⟧}⟩>
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add ... | {
"game_data": {
"answer": "<⟨{⟦⟨⟦({<{[⟨⟦{}()⟧⟩]⟦⟧⟨⟩[]⟦⟧}()>[]})⟧⟩⟧}⟩>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "<⟨{⟦⟨⟦({<{[⟨⟦{}()⟧⟩]⟦⟧⟨⟩[]⟦⟧}()>[]})⟧⟩⟧}⟩>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟨{⟦⟨⟦({<{[⟨⟦... |
logic-v2 | Let S = ">]]])⦄⟩>>⦄⟩⟧}]}⟩⦄⟩⟩" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "⟨⟨⦃⟨{[{⟦⟨⦃<<⟨⦃([[[<>]]])⦄⟩>>⦄⟩⟧}]}⟩⦄⟩⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 19,
"full_sequence": "⟨⟨⦃⟨{[{⟦⟨⦃<<⟨⦃([[[<>]]])⦄⟩>>⦄⟩⟧}]}⟩⦄⟩⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟨⦃⟨{[{⟦⟨⦃<<⟨⦃([[[<",... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ⟦⟧⟩<>)[][]{}<>⟧⟩>⟦⟧<>)[]<>⟦⟧⟩)]⟩⟩)()>⟦⟧⟦⟧{}⟦⟧
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "<(⟨⟨[(⟨(<⟨⟦(⟨⟦⟧⟩<>)[][]{}<>⟧⟩>⟦⟧<>)[]<>⟦⟧⟩)]⟩⟩)()>⟦⟧⟦⟧{}⟦⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "<(⟨⟨[(⟨(<⟨⟦(⟨⟦⟧⟩<>)[][]{}<>⟧⟩>⟦⟧<>)[]<>⟦⟧⟩)]⟩⟩)()>⟦⟧⟦⟧{}⟦⟧",
"n_types": 6,
"nesting_depth": 0,
... |
logic-v2 | Fill in the blank:
_____ + {}⟦⟧⟦⟧⟩<>]]⟧>}⟧}> = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<{⟦{<⟦[[⟨{}⟦⟧⟦⟧⟩<>]]⟧>}⟧}>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "<{⟦{<⟦[[⟨{}⟦⟧⟦⟧⟩<>]]⟧>}⟧}>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{⟦{<⟦[[⟨",
"prompt_name": "fill_in",
... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"⟧⟩⟧}>})>⟩}⟩}>"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`... | {
"game_data": {
"answer": "<{⟨{⟨<({<{⟦⟨⟦⟧⟩⟧}>})>⟩}⟩}>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "<{⟨{⟨<({<{⟦⟨⟦⟧⟩⟧}>})>⟩}⟩}>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{⟨{⟨<({<{⟦⟨⟦",
"prompt_name": "story",... |
logic-v2 | Q: What opening brackets should precede "[]}⟧>⟩]⟩" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨[⟨<⟦{[]}⟧>⟩]⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "⟨[⟨<⟦{[]}⟧>⟩]⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨[⟨<⟦{",
"prompt_name": "qa",
"prompt_variant": 6,
"... |
logic-v2 | Let S = "]]})}<>⟩})}}]}]])}]]}>⟩⟩}" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "{⟨⟨<{[[{([[{[{{({⟨{({[[]]})}<>⟩})}}]}]])}]]}>⟩⟩}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 23,
"full_sequence": "{⟨⟨<{[[{([[{[{{({⟨{({[[]]})}<>⟩})}}]}]])}]]}>⟩⟩}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: >]{}⟦⟧]⦆)<>⦅⦆}⟧⟧}}⦆⟩}]⟨⟩{}()⟦⟧⦃⦄⦃⦄[]⦃⦄⟦⟧[][]{}
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced s... | {
"game_data": {
"answer": "[{⟨⦅{{⟦⟦{(⦅[[<>]{}⟦⟧]⦆)<>⦅⦆}⟧⟧}}⦆⟩}]⟨⟩{}()⟦⟧⦃⦄⦃⦄[]⦃⦄⟦⟧[][]{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 14,
"full_sequence": "[{⟨⦅{{⟦⟦{(⦅[[<>]{}⟦⟧]⦆)<>⦅⦆}⟧⟧}}⦆⟩}]⟨⟩{}()⟦⟧⦃⦄⦃⦄[]⦃⦄⟦⟧[][]{}",
"n_types": 8,
"nesting_depth": 0,
... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: ⟧)]]()⟩[][]<>[]⦅⦆
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answ... | {
"game_data": {
"answer": "⟨[[(⟦⟧)]]()⟩[][]<>[]⦅⦆",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "⟨[[(⟦⟧)]]()⟩[][]<>[]⦅⦆",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟨[[(⟦",
"prompt_name": "reverse_perspective",
... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ()⦄⟧⟧⟩⦅⦆)>⟩[][]()
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra br... | {
"game_data": {
"answer": "⟨<(⟨⟦⟦⦃()⦄⟧⟧⟩⦅⦆)>⟩[][]()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 7,
"full_sequence": "⟨<(⟨⟦⟦⦃()⦄⟧⟧⟩⦅⦆)>⟩[][]()",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟨<(⟨⟦⟦⦃",
"prompt_name": "direct",
"pr... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: )]]>{}{}⟦⟧<>
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (t... | {
"game_data": {
"answer": "<[[()]]>{}{}⟦⟧<>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 4,
"full_sequence": "<[[()]]>{}{}⟦⟧<>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<[[(",
"prompt_name": "reverse_perspective",
"prompt_v... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ]))}][]()[][]{}[]<>[]<>
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any ex... | {
"game_data": {
"answer": "[{(([]))}][]()[][]{}[]<>[]<>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "[{(([]))}][]()[][]{}[]<>[]<>",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{(([",
"prompt_name": "direct",
... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"()>)}⟩]}"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{[⟨{(<()>)}⟩]}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "{[⟨{(<()>)}⟩]}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{[⟨{(<",
"prompt_name": "story",
"prompt_variant": 4,
... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: <>[]}()<><>)}
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answe... | {
"game_data": {
"answer": "{({<>[]}()<><>)}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 3,
"full_sequence": "{({<>[]}()<><>)}",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "{({",
"prompt_name": "puzzle",
"prompt_variant": 2,
... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: ))()
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (the compl... | {
"game_data": {
"answer": "(())()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 2,
"full_sequence": "(())()",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "((",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"see... |
logic-v2 | Q: What opening brackets should precede "()]]]]()})))))]])}]}})" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "({{[{([[((((({[[[[()]]]]()})))))]])}]}})",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 18,
"full_sequence": "({{[{([[((((({[[[[()]]]]()})))))]])}]}})",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({{[{([[((((({[[[... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ))()]]<>[]<><>>){}][]]>]}]
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backtick... | {
"game_data": {
"answer": "[{[<[[(<[[(())()]]<>[]<><>>){}][]]>]}]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "[{[<[[(<[[(())()]]<>[]<><>>){}][]]>]}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{[<[[(<[[((",
... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: })(){}()[])()()[]}]]{}()]))()))}[]){}[][]{}
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequ... | {
"game_data": {
"answer": "({(((([[[{(({})(){}()[])()()[]}]]{}()]))()))}[]){}[][]{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "({(((([[[{(({})(){}()[])()()[]}]]{}()]))()))}[]){}[][]{}",
"n_types": 3,
"nesting_depth": 0,
"ope... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: {}))]}<>{}⟨⟩<>[]
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answe... | {
"game_data": {
"answer": "{[(({}))]}<>{}⟨⟩<>[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 4,
"full_sequence": "{[(({}))]}<>{}⟨⟩<>[]",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{[((",
"prompt_name": "reverse_perspective",
"... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: }{}][]{}]())}]]]]))}{})[]()()[]()[]{}
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do ... | {
"game_data": {
"answer": "({(([[[[{([[{}{}][]{}]())}]]]]))}{})[]()()[]()[]{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "({(([[[[{([[{}{}][]{}]())}]]]]))}{})[]()()[]()[]{}",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix"... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: }]>}()⟨⟩()⟨⟩
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (t... | {
"game_data": {
"answer": "{<[{}]>}()⟨⟩()⟨⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 4,
"full_sequence": "{<[{}]>}()⟨⟩()⟨⟩",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "{<[{",
"prompt_name": "reverse_perspective",
"prompt_v... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ⟧}⦆{}⦃⦄)⟦⟧⟧>⟨⟩
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra brack... | {
"game_data": {
"answer": "<⟦(⦅{⟦⟧}⦆{}⦃⦄)⟦⟧⟧>⟨⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "<⟦(⦅{⟦⟧}⦆{}⦃⦄)⟦⟧⟧>⟨⟩",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "<⟦(⦅{⟦",
"prompt_name": "direct",
"prompt_vari... |
logic-v2 | Let S = ">{}))}}]}]]" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "[[{[{{((<>{}))}}]}]]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "[[{[{{((<>{}))}}]}]]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[[{[{{((<",
"prompt_name": "mathematical",
"pr... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: <>⦄⦄⟦⟧)⟨⟩}⦃⦄⟩⟦⟧⦃⦄⦃⦄⦃⦄
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final ... | {
"game_data": {
"answer": "⟨{(⦃⦃<>⦄⦄⟦⟧)⟨⟩}⦃⦄⟩⟦⟧⦃⦄⦃⦄⦃⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "⟨{(⦃⦃<>⦄⦄⟦⟧)⟨⟩}⦃⦄⟩⟦⟧⦃⦄⦃⦄⦃⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨{(⦃⦃",
"prompt_name": "reverse_perspect... |
logic-v2 | Let S = "()[]})()){}{}[]])>{}]()[]()]]}}]" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "[{{[[[<([(({()[]})()){}{}[]])>{}]()[]()]]}}]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "[{{[[[<([(({()[]})()){}{}[]])>{}]()[]()]]}}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{{[[[<([... |
logic-v2 | Let S = "⟧⟦⟧)" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "(⟦⟧⟦⟧)",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 2,
"full_sequence": "(⟦⟧⟦⟧)",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "(⟦",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 883... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"⟦⟧{}]⟩⟦⟧>⟧]}}}>"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answe... | {
"game_data": {
"answer": "<{{{[⟦<⟨[⟦⟧{}]⟩⟦⟧>⟧]}}}>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "<{{{[⟦<⟨[⟦⟧{}]⟩⟦⟧>⟧]}}}>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{{{[⟦<⟨[",
"prompt_name": "story",
"p... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ⦄<>{}>⦅⦆⟩)]⟧}⦄⦆⟧}⟩]⟧>}]⦆}
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks... | {
"game_data": {
"answer": "{⦅[{<⟦[⟨{⟦⦅⦃{⟦[(⟨<⦃⦄<>{}>⦅⦆⟩)]⟧}⦄⦆⟧}⟩]⟧>}]⦆}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 19,
"full_sequence": "{⦅[{<⟦[⟨{⟦⦅⦃{⟦[(⟨<⦃⦄<>{}>⦅⦆⟩)]⟧}⦄⦆⟧}⟩]⟧>}]⦆}",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "{⦅[{<⟦[⟨{... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: >}]<>⟦⟧
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "[{<>}]<>⟦⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 3,
"full_sequence": "[{<>}]<>⟦⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "[{<",
"prompt_name": "technical",
"prompt_variant": 3,
"seed... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: }⟩}⟩}{}><>⟩]])}(){}[]{}{}{}⟨⟩<>⟨⟩<>⟨⟩()<>
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "{([[⟨<{⟨{⟨{}⟩}⟩}{}><>⟩]])}(){}[]{}{}{}⟨⟩<>⟨⟩<>⟨⟩()<>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "{([[⟨<{⟨{⟨{}⟩}⟩}{}><>⟩]])}(){}[]{}{}{}⟨⟩<>⟨⟩<>⟨⟩()<>",
"n_types": 5,
"nesting_depth": 0,
"opening_pre... |
logic-v2 | Q: What opening brackets should precede "][]<>{})}]⟩]<>>]⟦⟧>>>>" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<<<<[<[⟨[{([][]<>{})}]⟩]<>>]⟦⟧>>>>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "<<<<[<[⟨[{([][]<>{})}]⟩]<>>]⟦⟧>>>>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<<<[<[⟨[{([",
"prompt_... |
logic-v2 | Q: What opening brackets should precede "){}[]()])()>[])[]{}>>])]}})}>}}>}]" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[{<{{<{({{[([<<(<([(){}[]()])()>[])[]{}>>])]}})}>}}>}]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 20,
"full_sequence": "[{<{{<{({{[([<<(<([(){}[]()])()>[])[]{}>>])]}})}>}}>}]",
"n_types": 4,
"nesting_depth": 0,
"opening... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ⦄⦆⟧⟧⟨⟩⦆<>⦅⦆⦃⦄⟩⦄⦆()()[]>>)]()⦅⦆⦃⦄⟨⟩⦅⦆⟦⟧
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do... | {
"game_data": {
"answer": "[(<<⦅⦃⟨⦅⟦⟦⦅⦃⦄⦆⟧⟧⟨⟩⦆<>⦅⦆⦃⦄⟩⦄⦆()()[]>>)]()⦅⦆⦃⦄⟨⟩⦅⦆⟦⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "[(<<⦅⦃⟨⦅⟦⟦⦅⦃⦄⦆⟧⟧⟨⟩⦆<>⦅⦆⦃⦄⟩⦄⦆()()[]>>)]()⦅⦆⦃⦄⟨⟩⦅⦆⟦⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix"... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: }{}>{}]]()[]<>}]
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `an... | {
"game_data": {
"answer": "[{[[<{}{}>{}]]()[]<>}]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "[{[[<{}{}>{}]]()[]<>}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{[[<{",
"prompt_name": "puzzle",
"prompt_... |
logic-v2 | Let S = ">{}}>]])))]>>]}}>]" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "[<{{[<<[((([[<{<>{}}>]])))]>>]}}>]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 16,
"full_sequence": "[<{{[<<[((([[<{<>{}}>]])))]>>]}}>]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<{{[<<[((([[<{<",
"pro... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: [][]}⦆]]⦆}]]⦆⦄})⟩⦄)⦄⦄))⟩⦄⟩}]])⟩}
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in ba... | {
"game_data": {
"answer": "{⟨([[{⟨⦃⟨((⦃⦃(⦃⟨({⦃⦅[[{⦅[[⦅{[][]}⦆]]⦆}]]⦆⦄})⟩⦄)⦄⦄))⟩⦄⟩}]])⟩}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 28,
"full_sequence": "{⟨([[{⟨⦃⟨((⦃⦃(⦃⟨({⦃⦅[[{⦅[[⦅{[][]}⦆]]⦆}]]⦆⦄})⟩⦄)⦄⦄))⟩⦄⟩}]])⟩}",
"n_types": 8,
"nesting_depth": 0,
... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: }<>)}][]>)]]]]><>()()>[]<>]}[])]]
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide... | {
"game_data": {
"answer": "[[({[<<[[[[(<[{({}<>)}][]>)]]]]><>()()>[]<>]}[])]]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"full_sequence": "[[({[<<[[[[(<[{({}<>)}][]>)]]]]><>()()>[]<>]}[])]]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix"... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: )])])]])}}}])
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "([{{{([[([([()])])]])}}}])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "([{{{([[([([()])])]])}}}])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([{{{([[([([(",
"prompt_name": "technic... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ]}]>>()[]{}{}{}()>})}}>)]})])}]
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not ad... | {
"game_data": {
"answer": "[{([({[(<{{({<<<[{[]}]>>()[]{}{}{}()>})}}>)]})])}]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 19,
"full_sequence": "[{([({[(<{{({<<<[{[]}]>>()[]{}{}{}()>})}}>)]})])}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix"... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ()()[]()]>]}]]
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "[[{[<[()()[]()]>]}]]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "[[{[<[()()[]()]>]}]]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[[{[<[",
"prompt_name": "technical",
"prompt_v... |
logic-v2 | Q: What opening brackets should precede "<><>⟨⟩)>" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<(<><>⟨⟩)>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 2,
"full_sequence": "<(<><>⟨⟩)>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<(",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 50007... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ][]]{}{}()]})})})]])
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra... | {
"game_data": {
"answer": "([[({({({[[[][]]{}{}()]})})})]])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "([[({({({[[[][]]{}{}()]})})})]])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([[({({({[[[",
"prompt_name... |
logic-v2 | Q: What opening brackets should precede "⟧⟨⟩⦃⦄⟨⟩⟦⟧>[]}⦄⟩⟧⦃⦄()⦃⦄[]()⟨⟩⦃⦄{}⦃⦄>)⟧⟩" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨⟦(<⟦⟨⦃{<⟦⟧⟨⟩⦃⦄⟨⟩⟦⟧>[]}⦄⟩⟧⦃⦄()⦃⦄[]()⟨⟩⦃⦄{}⦃⦄>)⟧⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "⟨⟦(<⟦⟨⦃{<⟦⟧⟨⟩⦃⦄⟨⟩⟦⟧>[]}⦄⟩⟧⦃⦄()⦃⦄[]()⟨⟩⦃⦄{}⦃⦄>)⟧⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨... |
logic-v2 | Let S = "{}⟦⟧>" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "<{}⟦⟧>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 1,
"full_sequence": "<{}⟦⟧>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 8253... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"⦄>⟧>⟩⦃⦄⟦⟧⦃⦄<>⟩)⟨⟩}{}]<>⦃⦄⟧⟩⟦⟧⟨⟩[]⦃⦄"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in b... | {
"game_data": {
"answer": "⟨⟦[{(⟨⟨<⟦<⦃⦄>⟧>⟩⦃⦄⟦⟧⦃⦄<>⟩)⟨⟩}{}]<>⦃⦄⟧⟩⟦⟧⟨⟩[]⦃⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "⟨⟦[{(⟨⟨<⟦<⦃⦄>⟧>⟩⦃⦄⟦⟧⦃⦄<>⟩)⟨⟩}{}]<>⦃⦄⟧⟩⟦⟧⟨⟩[]⦃⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟦[{(... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"{}){}])()}}}]]])"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answ... | {
"game_data": {
"answer": "([[[{{{([({}){}])()}}}]]])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "([[[{{{([({}){}])()}}}]]])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([[[{{{([(",
"prompt_name": "story",
... |
logic-v2 | Q: What opening brackets should precede "}>>)>" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<(<<{}>>)>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "<(<<{}>>)>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<(<<{",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 92... |
logic-v2 | Q: What opening brackets should precede ")]{}[]]}[])}()])()" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "([{({[[()]{}[]]}[])}()])()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 8,
"full_sequence": "([{({[[()]{}[]]}[])}()])()",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([{({[[(",
"prompt_name": "qa",
"p... |
logic-v2 | Q: What opening brackets should precede "(){}{}}]()])]}>⟩>)}>⟩⟩}" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{⟨⟨<{(<⟨<{[([[{(){}{}}]()])]}>⟩>)}>⟩⟩}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 15,
"full_sequence": "{⟨⟨<{(<⟨<{[([[{(){}{}}]()])]}>⟩>)}>⟩⟩}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{⟨⟨<{(<⟨<{[([[{",
... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"><>)><>>>>}}}()[]}<>()}]]]}}]<>"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backt... | {
"game_data": {
"answer": "[{{[[[{{{{{<<<<(<><>)><>>>>}}}()[]}<>()}]]]}}]<>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"full_sequence": "[{{[[[{{{{{<<<<(<><>)><>>>>}}}()[]}<>()}]]]}}]<>",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[... |
logic-v2 | Q: What opening brackets should precede "}]⟩}>])}>})⟩)⟩}]>}()}()<>(){}⟨⟩<>()" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{{<[{⟨(⟨({<{([<{⟨[{}]⟩}>])}>})⟩)⟩}]>}()}()<>(){}⟨⟩<>()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 19,
"full_sequence": "{{<[{⟨(⟨({<{([<{⟨[{}]⟩}>])}>})⟩)⟩}]>}()}()<>(){}⟨⟩<>()",
"n_types": 5,
"nesting_depth": 0,
"opening... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: )>]]⟩⦄⦆}]>
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (the... | {
"game_data": {
"answer": "<[{⦅⦃⟨[[<()>]]⟩⦄⦆}]>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "<[{⦅⦃⟨[[<()>]]⟩⦄⦆}]>",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "<[{⦅⦃⟨[[<(",
"prompt_name": "reverse_perspective",
... |
logic-v2 | Fill in the blank:
_____ + )>()]}{}(){}[])>]<>>}>] = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[<{<[<({[<()>()]}{}(){}[])>]<>>}>]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "[<{<[<({[<()>()]}{}(){}[])>]<>>}>]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<{<[<({[<(",
"prompt_n... |
logic-v2 | Let S = "⟧}]⟦⟧])⦄()⟧)⟩⟧⟧⟧}⟩⟧}⦄⦄⟧⟩⦄" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "⦃⟨⟦⦃⦃{⟦⟨{⟦⟦⟦⟨(⟦⦃([[{⟦⟧}]⟦⟧])⦄()⟧)⟩⟧⟧⟧}⟩⟧}⦄⦄⟧⟩⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 21,
"full_sequence": "⦃⟨⟦⦃⦃{⟦⟨{⟦⟦⟦⟨(⟦⦃([[{⟦⟧}]⟦⟧])⦄()⟧)⟩⟧⟧⟧}⟩⟧}⦄⦄⟧⟩⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃⟨⟦⦃⦃... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"}⟨⟩⟩{}}][][]>{}<>⟨⟩⟩>}}}]]]⟩)⟩}⟩}}"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in ba... | {
"game_data": {
"answer": "{{⟨{⟨(⟨[[[{{{<⟨<[{⟨{}⟨⟩⟩{}}][][]>{}<>⟨⟩⟩>}}}]]]⟩)⟩}⟩}}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 20,
"full_sequence": "{{⟨{⟨(⟨[[[{{{<⟨<[{⟨{}⟨⟩⟩{}}][][]>{}<>⟨⟩⟩>}}}]]]⟩)⟩}⟩}}",
"n_types": 5,
"nesting_depth": 0,
"opening... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ⦄⟦⟧⟨⟩}⦆⦆>]⟩⦆}⦄}⦆⦄
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `a... | {
"game_data": {
"answer": "⦃⦅{⦃{⦅⟨[<⦅⦅{⦃⦄⟦⟧⟨⟩}⦆⦆>]⟩⦆}⦄}⦆⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "⦃⦅{⦃{⦅⟨[<⦅⦅{⦃⦄⟦⟧⟨⟩}⦆⦆>]⟩⦆}⦄}⦆⦄",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦃⦅{⦃{⦅⟨[<⦅⦅{⦃",
"prompt_name": ... |
logic-v2 | Q: What opening brackets should precede "<>[]<>)}" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{(<>[]<>)}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 2,
"full_sequence": "{(<>[]<>)}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{(",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 66715... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ⟩)>⟦⟧>}})]()<>)⦄⟩⦃⦄[]{}<>⟨⟩{}(){}{}{}⟦⟧⟨⟩<>
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequ... | {
"game_data": {
"answer": "⟨⦃([({{<<(⟨⟩)>⟦⟧>}})]()<>)⦄⟩⦃⦄[]{}<>⟨⟩{}(){}{}{}⟦⟧⟨⟩<>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "⟨⦃([({{<<(⟨⟩)>⟦⟧>}})]()<>)⦄⟩⦃⦄[]{}<>⟨⟩{}(){}{}{}⟦⟧⟨⟩<>",
"n_types": 7,
"nesting_depth": 0,
"opening... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ⦆⟧)]<>⦅⦆⟨⟩<>[]{}⟧⦄⟩⦃⦄>⦄()⟨⟩⟨⟩})<>>
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not... | {
"game_data": {
"answer": "<({⦃<⟨⦃⟦[(⟦⦅⦆⟧)]<>⦅⦆⟨⟩<>[]{}⟧⦄⟩⦃⦄>⦄()⟨⟩⟨⟩})<>>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "<({⦃<⟨⦃⟦[(⟦⦅⦆⟧)]<>⦅⦆⟨⟩<>[]{}⟧⦄⟩⦃⦄>⦄()⟨⟩⟨⟩})<>>",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "<({⦃<... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: }<>])>]>⟩⟩⟩⟧]}}>]}⟧⟧})>⟧>
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any ... | {
"game_data": {
"answer": "<⟦<({⟦⟦{[<{{[⟦⟨⟨⟨<[<([{}<>])>]>⟩⟩⟩⟧]}}>]}⟧⟧})>⟧>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 23,
"full_sequence": "<⟦<({⟦⟦{[<{{[⟦⟨⟨⟨<[<([{}<>])>]>⟩⟩⟩⟧]}}>]}⟧⟧})>⟧>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ⟩⟩{}⟩⟧}{})⟩[]){}⟩]}]]}})⟧⟧>
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add an... | {
"game_data": {
"answer": "<⟦⟦({{[[{[⟨(⟨({⟦⟨⟨⟨⟩⟩{}⟩⟧}{})⟩[]){}⟩]}]]}})⟧⟧>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 19,
"full_sequence": "<⟦⟦({{[[{[⟨(⟨({⟦⟨⟨⟨⟩⟩{}⟩⟧}{})⟩[]){}⟩]}]]}})⟧⟧>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟦⟦({... |
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