env stringclasses 1
value | prompt stringlengths 203 478 | extra dict |
|---|---|---|
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... | {
"game_data": {
"answer": "⟦⟨⟦⟦<⦃{{⟨⦅⦅<⦃⟦⟦⦃[(⟨⦅(<⦅<>⦆<>[]>)⦆⟩())⟦⟧⦅⦆]⦄()⟧⟧⦄>⦆⦆⟩}}⦄>⟧⟧⟩⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 23,
"full_sequence": "⟦⟨⟦⟦<⦃{{⟨⦅⦅<⦃⟦⟦⦃[(⟨⦅(<⦅<>⦆<>[]>)⦆⟩())⟦⟧⦅⦆]⦄()⟧⟧⦄>⦆⦆⟩}}⦄>⟧⟧⟩⟧",
"n_types": 8,
"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 any ext... | {
"game_data": {
"answer": "⟨⟨([[{⟨(<<{<<(⦃<⟨[(⟨<()>⟩)]⟩>⦄)>>}>>)⟩}]])⟩⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 22,
"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 fin... | {
"game_data": {
"answer": "<<{(<⟦⟦({<>})⟧⟧⟦⟧>⟦⟧{}⟨⟩)}>[]><>⟦⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "<<{(<⟦⟦({<>})⟧⟧⟦⟧>⟦⟧{}⟨⟩)}>[]><>⟦⟧",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<{(<⟦⟦({<",
"prompt_na... |
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... | {
"game_data": {
"answer": "(⟨<⦃{(⟦[⟨⟩]⟧)}⦄⟦⟧⦅⦆[]>⟩)[]⟨⟩{}⟨⟩⟨⟩[]⟨⟩⟨⟩<>{}[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "(⟨<⦃{(⟦[⟨⟩]⟧)}⦄⟦⟧⦅⦆[]>⟩)[]⟨⟩{}⟨⟩⟨⟩[]⟨⟩⟨⟩<>{}[]",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "(⟨<⦃{(... |
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": 4,
"nesting_depth": 0,
"opening_prefix": "[<[<[<[((",
"prompt_name": "fill... |
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": 13,
"full_sequence": "[{[{(<<[([{({})}])]>>)}]}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{[{(<<[([{({",
"prompt_name": "puzzle"... |
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": 6,
"full_sequence": "[⟦⟦⦅(())⦆⟧⟧]",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "[⟦⟦⦅((",
"prompt_name": "mathematical",
"prompt_variant": 5,
... |
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": 7,
"full_sequence": "⦃[⦅[[([⟨⟩{}]){}]]{}⦆]⦄⦅⦆⟨⟩⟦⟧<>⟦⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦃[⦅[[([",
"prompt_name": "fi... |
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
Plea... | {
"game_data": {
"answer": "[[((<({{[[<{[({{<()>{}}()})]}>{}{}]{}<>]<>}<>()}())>)<>)]<>]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"full_sequence": "[[((<({{[[<{[({{<()>{}}()})]}>{}{}]{}<>]<>}<>()}())>)<>)]<>]",
"n_types": 4,
"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 ... | {
"game_data": {
"answer": "{([[<⦃⦃⦅⦅⦆⦆⦄⦅⦆⦄>]]()[]())}⟦⟧⦅⦆[]⦃⦄<>[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "{([[<⦃⦃⦅⦅⦆⦆⦄⦅⦆⦄>]]()[]())}⟦⟧⦅⦆[]⦃⦄<>[]",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "{([[<⦃⦃⦅⦅",
"pro... |
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": 4,
"nesting_depth": 0,
"opening_prefix": "[({",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 40... |
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": 10,
"full_sequence": "⟦⟦⦅⦃⟨⦃<⦅⦃(<>)⦄{}{}⦆>⦄⟩⦄⦆⟧⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟦⟦⦅⦃⟨⦃<⦅⦃(",
"prompt_name": "fill_in",
... |
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": 13,
"full_sequence": "⟨⟨{⟨⟨⟦([{{[<⟨⟦⟧⟩>]}⟨⟩}()⟨⟩(){}])⟧⟩⟩}⟩<>⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟨{⟨⟨⟦([{{[<⟨",
... |
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": 5,
"full_sequence": "([([()()]){}])()[][](){}[][]",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([([(",
"prompt_name": "fill_in",
... |
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": 3,
"nesting_depth": 0,
... |
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": 16,
"full_sequence": "{[⟨[(([{<[{[[⟨⟨<[]>{}()()⟩⟩]]⟨⟩⟨⟩[]}⟨⟩]()>[]}]))]⟩]}",
"n_types": 5,
"nesting_depth": 0,
"opening_pre... |
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 ... | {
"game_data": {
"answer": "([[{[[{(({{{{}[]}}[][]})[])}]]}]])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "([[{[[{(({{{{}[]}}[][]})[])}]]}]])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([[{[[{(({{{{",
"prompt... |
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 e... | {
"game_data": {
"answer": "<⟨⟦([⟨⟦⟦⟨⟦{[⟦<⟦{⟨⟨⟦[⟦⟧⟨⟩]⟧⟩⟩}⟧>⟧]}⟧⟩⟧⟧⟩])⟧⟩>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 20,
"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": 5,
"full_sequence": "{[{{⟨⟩}()}]<>⟨⟩}()",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{[{{⟨",
"prompt_name": "mathematical",
"prompt_var... |
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": 11,
"full_sequence": "[<{(<{<([[{}]{}]{}())>{}}{}<>[]>)}>]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<{(<{<([[{",
"prom... |
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": 6,
"full_sequence": "{<(⟨{{{}}}{}⟩⟨⟩)()>[]}(){}<>()[]()",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{<(⟨{{",
"prompt_name": ... |
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": 16,
"full_sequence": "({{([([{{{[[{({[()[]]()})}][]]{}}()}}])])}})",
"n_types": 3,
"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 backtick... | {
"game_data": {
"answer": "({[({{([[[([[((({{[({[{((({})))}]})]}})))]])]]])}})]})",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 26,
"full_sequence": "({[({{([[[([[((({{[({[{((({})))}]})]}})))]])]]])}})]})",
"n_types": 3,
"nesting_depth": 0,
"opening... |
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": 25,
"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": 17,
"full_sequence": "{⟨⟨[[(⟨⟨⟨⟨[([(<{<{}>()}>){}])]⟩⟩⟩⟩)]]⟩⟩}",
"n_types": 5,
"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": 3,
"nesting_depth": 0,
"opening_prefix": "(({",
"prompt_name": "mathematical",
"prompt_variant": 5,
... |
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": 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": 11,
"full_sequence": "[{<[<([<[[{}]{}{}]>])>]>}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{<[<([<[[{",
"prompt_name": "technical... |
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": 7,
"full_sequence": "⦃[⦅⟨⟨{()}⟩⟩⦅⦆⦆]⦄<>⟨⟩⦅⦆(){}<>⟨⟩⦃⦄",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦃[⦅⟨⟨{(",
"prompt_name": "fi... |
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": 7,
"full_sequence": "([({({[{}()][][]})})])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([({({[",
"prompt_name": "reverse_perspective",
... |
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": 7,
"nesting_depth": 0,
"opening_prefix": "⟨<(<[⦃⟨",
"prompt_na... |
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": 13,
"full_sequence": "<<<⟨⟦((⟨<<⟨[{}]⟩⟦⟧>[]>⟩))⟧⟩>>>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<<⟨⟦((⟨<<⟨[{",
"prompt_name": ... |
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": 6,
"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 ... | {
"game_data": {
"answer": "((({[]}(){}{})))[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 4,
"full_sequence": "((({[]}(){}{})))[]",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "((({",
"prompt_name": "reverse_perspective",
"prom... |
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": 16,
"full_sequence": "[[[[{([<{[(<([{(<>)}]){}>){}]}>])}]]]][]{}(){}{}[]{}[](){}()",
"n_types": 4,
"nesting_depth": 0,
... |
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": 8,
"full_sequence": "⦅[<⟨<⟨<{[]}>⟩>⟩{}⦃⦄>]⦆()<>{}⦃⦄⟦⟧<>()",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦅[<⟨<⟨<{",
"prompt_n... |
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": 3,
"full_sequence": "((()){}){}{}",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(((",
"prompt_name": "fill_in",
"prompt_variant": 7,
"se... |
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": 4,
"nesting_depth": 0,
"opening_prefix": "[<<<<[{[[([{((",
"prompt_na... |
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 lik... | {
"game_data": {
"answer": "[[[[([[[({<<{{<[{}]><>()}}>>})]]])]]]]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"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": 13,
"full_sequence": "⟨{⟨{<[⟨{[{⦃[()]⦄}]}⟩]>}⟩}⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨{⟨{<[⟨{[{⦃[(",
"prompt_name": "mathema... |
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": 21,
"full_sequence": "({[{([[[{[[[{([[{({({}()[])})}]])}]{}()]]()}]]])}]})",
"n_types": 3,
"nesting_depth": 0,
"opening_pre... |
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": 4,
"nesting_depth": 0,
"opening... |
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": 4,
"full_sequence": "(([[]])){}",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(([[",
"prompt_name": "fill_in",
"prompt_variant": 7,
"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": 14,
"full_sequence": "{[[⟨{{{({(<[[⟨⟩]]>[]()⟨⟩)<>})<>}}()⟨⟩}⟩]][]⟨⟩{}()}",
"n_types": 5,
"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 extra bracket pairs... | {
"game_data": {
"answer": "[({(())})]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 4,
"full_sequence": "[({(())})]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[({(",
"prompt_name": "direct",
"prompt_variant": 0,
"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 answer (t... | {
"game_data": {
"answer": "⟨[⦃⦄{}<>]⟩()⟦⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 2,
"full_sequence": "⟨[⦃⦄{}<>]⟩()⟦⟧",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨[",
"prompt_name": "reverse_perspective",
"prompt_variant... |
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": 25,
"full_sequence": "⟨⦃<⟨<⟦⟨⟨{⟦⟨([<⦃{<[⟦(⦃⟦⦃⟨⟦⟧⟩{}⦄⟧⦄)⟧⟨⟩[]⟨⟩][]>}⦄>])⟩⟧}⟩⟩⟧>⟩>⦄⟩",
"n_types": 7,
"nesting_depth": 0,
... |
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 sequenc... | {
"game_data": {
"answer": "<{⟦⟨{<⟨{[⦃⦃⟦[{{⟦<⦅⦆>⟧}[]}]⟨⟩{}⟧⟨⟩⦄⦄]}⟩><>}⟩{}<>⟦⟧{}⟧⟦⟧}>[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 18,
"full_sequence": "<{⟦⟨{<⟨{[⦃⦃⟦[{{⟦<⦅⦆>⟧}[]}]⟨⟩{}⟧⟨⟩⦄⦄]}⟩><>}⟩{}<>⟦⟧{}⟧⟦⟧}>[]",
"n_types": 8,
"nesting_depth": 0,
... |
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 | 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": 7,
"nesting_depth": 0,
"opening_prefix": "⟨<{⟨{⟦{⟨⟦[⦃⟨",
"pro... |
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": 10,
"full_sequence": "[{<({[[<[<>]><>]]})>}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{<({[[<[<",
"prompt_name": "reverse_perspectiv... |
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": 13,
"full_sequence": "⟨<<(⟦⟨⟦⟨⦃(⟦⟨{⦃⦄⟨⟩}⟩⟧<>{})⦄⟩⟧⟩⟧)>>⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨<<(⟦⟨⟦⟨⦃(⟦⟨{",
"prompt... |
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": 3,
"nesting_depth": 0,
"opening_prefix": "(([{{{",
"prompt_name": "technical",
"prompt_v... |
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": 26,
"full_sequence": "[<([<{<(<[(<[({<[<({[[[((<>))]]]})>]>})]>)]>)>}>])>]",
"n_types": 4,
"nesting_depth": 0,
"opening_pre... |
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 sequenc... | {
"game_data": {
"answer": "((([[[{[{({((((())())){})})}{}]()}][]]()]{})())[])[][][]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 16,
"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... | {
"game_data": {
"answer": "<{((({}[]))⟦⟧)<><>()}>()<>[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "<{((({}[]))⟦⟧)<><>()}>()<>[]",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{((({",
"prompt_name": "reverse_per... |
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": 8,
"nesting_depth": 0,
"opening_prefix": "{<⦃{⦅⦃",
"prompt_name": "technical",
"prompt_variant": 3,
... |
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": 3,
"nesting_depth": 0,
"ope... |
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": 5,
"full_sequence": "<{⟦⟨⟦⟧()⟩⟧}>⟨⟩{}[]()<>()",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{⟦⟨⟦",
"prompt_name": "fill_in",
"pro... |
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": 12,
"full_sequence": "({[[{[([({((()[])()[][]())}){}]())]}]]})",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({[[{[([({((",
... |
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": 3,
"full_sequence": "[([][])][]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[([",
"prompt_name": "fill_in",
"prompt_variant": 7,
"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 f... | {
"game_data": {
"answer": "({[({[{{({({(({{({({[{}[]][]})})}}))})})}}]})]})",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 22,
"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 (the compl... | {
"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_variant": 1,
... |
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": 10,
"full_sequence": "{(⟨[{⟨⟨[⦃<⟨⟩>⦄]⟩⟩}]⟩)}⟦⟧[]⟦⟧<><>⟦⟧{}⟨⟩(){}⦅⦆",
"n_types": 8,
"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": 7,
"full_sequence": "<⟨⦃⟦⦅[[⦅⦆⦅⦆]]⦆⟧⦄⟩>",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "<⟨⦃⟦⦅[[",
"prompt_name": "story",
"prompt_variant"... |
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 provi... | {
"game_data": {
"answer": "({(((([({{}[]})][])[])))})[]{}()()[][]{}{}()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "({(((([({{}[]})][])[])))})[]{}()()[][]{}{}()",
"n_types": 3,
"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": 6,
"full_sequence": "<[{{⟨(())⟩<>}}]<>>{}",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<[{{⟨(",
"prompt_name": "mathematical",
"promp... |
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": 10,
"full_sequence": "<⟦⟦⟨(⟦[{([])}{}⟨⟩]⟧)⟩⟧⟧>()⟨⟩<>⟦⟧{}⟦⟧{}⟨⟩{}⟨⟩{}{}⟦⟧[]",
"n_types": 6,
"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": 7,
"full_sequence": "(({[{{(){}}()}]}))",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(({[{{(",
"prompt_name": "qa",
"prompt_variant": 6... |
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 lik... | {
"game_data": {
"answer": "([(([[][]]())())]{})[](){}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "([(([[][]]())())]{})[](){}",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([(([",
"prompt_name": "puzzle",
"... |
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": 8,
"full_sequence": "{[[<<[((){})]>>]]}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{[[<<[((",
"prompt_name": "puzzle",
"prompt_varian... |
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": 22,
"full_sequence": "⟨⟦<⦃[[[⦃(⦃[[⟦⦃[⦃⟨[{{{[⟦⟧]}⦃⦄}}]<>⟩⦄][]⦄⟧]]⦄)⦄]]]⦄>⟧⟩",
"n_types": 7,
"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 ext... | {
"game_data": {
"answer": "{<{(⟨[({⟨()⟩[]⟨⟩⟨⟩})<>]⟨⟩<>⟩)}>}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "{<{(⟨[({⟨()⟩[]⟨⟩⟨⟩})<>]⟨⟩<>⟩)}>}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{<{(⟨[({⟨(",
"prompt_name":... |
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... | {
"game_data": {
"answer": "⟨{⟦{<⟦⟨<⟦⦃⦃{⟨⦅[[⦅⦃⦅⟨⟩⦆⦄⦆⦅⦆]⦃⦄]⦆⟩}⦄⟨⟩⦄[]⟨⟩⟧()>{}⟦⟧⟨⟩⟩⟧>}⟧}⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 19,
"full_sequence": "⟨{⟦{<⟦⟨<⟦⦃⦃{⟨⦅[[⦅⦃⦅⟨⟩⦆⦄⦆⦅⦆]⦃⦄]⦆⟩}⦄⟨⟩⦄[]⟨⟩⟧()>{}⟦⟧⟨⟩⟩⟧>}⟧}⟩",
"n_types": 8,
"nesting_depth": 0,
... |
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": 5,
"full_sequence": "(([({{}()})]))",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(([({",
"prompt_name": "puzzle",
"prompt_variant": 2,
... |
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": 6,
"full_sequence": "<[⟨⟨<<><>>⟩⟩]>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<[⟨⟨<<",
"prompt_name": "fill_in",
"prompt_variant": 7,
... |
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": 3,
"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 `an... | {
"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 | 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": 3,
"full_sequence": "<(⟨⟩)[]>[]",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<(⟨",
"prompt_name": "puzzle",
"prompt_variant": 2,
"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": 23,
"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 any extra brack... | {
"game_data": {
"answer": "⟨⟨(⟨<⦅<()>⦆>⟩)⟩⟩⟨⟩⦅⦆<>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 8,
"full_sequence": "⟨⟨(⟨<⦅<()>⦆>⟩)⟩⟩⟨⟩⦅⦆<>",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟨⟨(⟨<⦅<(",
"prompt_name": "direct",
"promp... |
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 c... | {
"game_data": {
"answer": "(([()])()[])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 4,
"full_sequence": "(([()])()[])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(([(",
"prompt_name": "reverse_perspective",
"prompt_variant":... |
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": 13,
"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 `ans... | {
"game_data": {
"answer": "[{<[({([{[{}]}])}[])]<>>}]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "[{<[({([{[{}]}])}[])]<>>}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{<[({([{[{",
"prompt_name": "puzzle",
... |
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": 17,
"full_sequence": "<⟨⟨⟨[⟨⟨((⟨⟨[(⟨(⟨⟨⟩()⟩)⟩)]⟨⟩⟩⟨⟩⟩))⟦⟧<>⟩⟩]⟩⟩⟩>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟨⟨⟨[⟨⟨((... |
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": 6,
"full_sequence": "[[<<{(())}>>]]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[[<<{(",
"prompt_name": "fill_in",
"prompt_variant": 7,
... |
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": 5,
"nesting_depth": 0,
"opening_prefix": "{{⟨{⟨<⟨⟨",
"prompt_name": "qa",
"prompt_va... |
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... | {
"game_data": {
"answer": "⟦[⦅⦅⟨⦃([⟨(<⦅⟨⦃⦅⟨⦃[⦅<>⦆⟦⟧⟨⟩⟦⟧()]⦄⟩⦆⦄⟩⦆>)⟩])⦄⟩⦆⦆]⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 20,
"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... | {
"game_data": {
"answer": "<{(⟨[()]⟩)}[]{}>{}<>{}{}()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "<{(⟨[()]⟩)}[]{}>{}<>{}{}()",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{(⟨[(",
"prompt_name": "puzzle",
... |
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": 10,
"full_sequence": "([((({([{[]}][])}))[])][])[]()()()[]",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([((({([{[",
"promp... |
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": 14,
"full_sequence": "<<<⟦(⟦[{(<⟨<[(())]()()>⟩>)}{}]⟧)⟧>>>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<<⟦(⟦[{(<⟨<[(",
"p... |
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": 5,
"nesting_depth": 0,
"opening_prefix": "{{⟨{{([<⟨[⟨<[",
"prompt_name": "story",... |
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": 25,
"full_sequence": "⦃⟨⟦⦃<[⦃⟨{⟨[{<{⟨<(⟨<⦃<⟨(<⟨⟩⟨⟩>)⟩>⦄>⟩)>⟩}>}]⟩}⟩⦄]>⦄⟧⟩⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_pre... |
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
Plea... | {
"game_data": {
"answer": "(({{{(([{((){}()())[]}]{}))[]{}}[]}[]})){}[]()[]{}[]{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "(({{{(([{((){}()())[]}]{}))[]{}}[]}[]})){}[]()[]{}[]{}",
"n_types": 3,
"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 prov... | {
"game_data": {
"answer": "<⟦⟨[⟦⟦(<⟦{[⟦<{⟨⟨⟩⟩}>⟧][]}⟧>){}⟧⟧]⟩⟧>[]{}⟨⟩[]{}[]{}<>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 16,
"full_sequence": "<⟦⟨[⟦⟦(<⟦{[⟦<{⟨⟨⟩⟩}>⟧][]}⟧>){}⟧⟧]⟩⟧>[]{}⟨⟩[]{}[]{}<>",
"n_types": 6,
"nesting_depth": 0,
"opening_pre... |
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": 13,
"full_sequence": "[{({{((<({{{[]}{}}})>))}})}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{({{((<({{{[",
"prompt_name": "rev... |
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": 25,
"full_sequence": "([[{{[{({{([{(({[{{{{[({[[][]()()]}{})]}}}}]}))}])}})}]}}]])",
"n_types": 3,
"nesting_depth": 0,
... |
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": 5,
"nesting_depth": 0,
"ope... |
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": 8,
"full_sequence": "<⟨({<{(⟦⟧{})}>⟨⟩})⟩>()⟨⟩()⟨⟩()⟦⟧⟦⟧[]⟦⟧",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟨({<{(⟦",
"prom... |
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 bracket ... | {
"game_data": {
"answer": "(([(([]{}()))]))",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "(([(([]{}()))]))",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(([((",
"prompt_name": "direct",
"prompt_variant": 0,
... |
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