env stringclasses 1
value | prompt stringlengths 203 478 | extra dict |
|---|---|---|
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": 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 ... | {
"game_data": {
"answer": "⟦{⟨⟦(⦃<⦅⦆>⦄⟦⟧)⟧⟩}()⟧()⟨⟩⟦⟧{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 7,
"full_sequence": "⟦{⟨⟦(⦃<⦅⦆>⦄⟦⟧)⟧⟩}()⟧()⟨⟩⟦⟧{}",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟦{⟨⟦(⦃<",
"prompt_name": "story",
... |
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": 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": 2,
"full_sequence": "⟨(⦃⦄)⟩[][]",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨(",
"prompt_name": "technical",
"prompt_variant": 3,
"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": 9,
"full_sequence": "[⟦([⟨⟦(⦅⦅⟦⟧⦆⦆){}⦃⦄⟧⦃⦄⟩]<>)⟧{}⟦⟧<>]⟨⟩<>[]",
"n_types": 8,
"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 yo... | {
"game_data": {
"answer": "⟨⟦{((⦃[{⟦⟦[⟦⦃[⦃{{⦃{}⦄}}⦄[]⟨⟩]⟨⟩[]{}⦄⟧]⟧⟧}]⦄))}⟧⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 18,
"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 you... | {
"game_data": {
"answer": "⟨⟨<⟨(⟨{[{[{(⟨<⦃⦄{}>⟩)}]}]}⟩⦃⦄)⟦⟧[]⟦⟧⟦⟧⟩><>⟩⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 15,
"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": 9,
"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": 5,
"full_sequence": "{{({<<>()>})<>}}⟨⟩<>⟨⟩()",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{{({<",
"prompt_name": "mathematical",
... |
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": 4,
"full_sequence": "[{(()[]){}}<>[]][]{}()",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{((",
"prompt_name": "direct",
"prompt_va... |
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 not ... | {
"game_data": {
"answer": "[<([[{[{{<[({<[<<{<{(<([(<>{}())<>])>)}>}>>]>})]>}}]}]])>]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 25,
"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 ... | {
"game_data": {
"answer": "{{({<((⟨(⟨{⟨[<({<(⟨⟨⟩[]⟩)>(){}}()()<>)>]⟩}⟩)⟩))>})}}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 19,
"full_sequence": "{{({<((⟨(⟨{⟨[<({<(⟨⟨⟩[]⟩)>(){}}()()<>)>]⟩}⟩)⟩))>})}}",
"n_types": 5,
"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": 7,
"full_sequence": "⦃[<⦃⦃⦃<>⦄()⟦⟧⦄⦄()>]⟨⟩[]⦄⟨⟩()⦅⦆[]",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦃[<⦃⦃⦃<",
"prompt_name": "te... |
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": 3,
"nesting_depth": 0,
"opening_prefix": "([([[({{",
"prompt_name": "mathematical"... |
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": 4,
"nesting_depth": 0,
"opening_prefix": "[{<<((({<{",
"prompt_name": "qa",
"pr... |
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": 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 extra br... | {
"game_data": {
"answer": "⟨[(⟨⟦⟨⟩⟧⟩)]⦃⦄⟩⟦⟧⟦⟧<>⦅⦆",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "⟨[(⟨⟦⟨⟩⟧⟩)]⦃⦄⟩⟦⟧⟦⟧<>⦅⦆",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟨[(⟨⟦",
"prompt_name": "direct",
"prompt_v... |
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": 19,
"full_sequence": "⟨{⦅⟨{⦃⦅(⟨⦃(⦅⟨⟨⟨<⟦{⦃⦄}⟧>⟩<>{}{}⟩⟩⦆)⦄⟩)⦆⦄⦅⦆()}⟩⦆{}}⟦⟧⟩",
"n_types": 8,
"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 `answer`. | {
"game_data": {
"answer": "{(())<>}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 2,
"full_sequence": "{(())<>}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{(",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 189867... |
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": 15,
"full_sequence": "([{[(((([([[[(({}))]]])]))))]}])",
"n_types": 3,
"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": 3,
"full_sequence": "[(<>)]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[(<",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 100385404,
... |
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": 3,
"nesting_depth": 0,
"opening_prefix": "([{[[{({[",
"prompt_name": "mathematical",
... |
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": 6,
"full_sequence": "<{[{(⟦⟨⟩[]⟦⟧⟧)[]()}]}>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{[{(⟦",
"prompt_name": "story",
"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": 16,
"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 pair... | {
"game_data": {
"answer": "<([⟦⟧]{})>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 3,
"full_sequence": "<([⟦⟧]{})>",
"n_types": 6,
"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 pr... | {
"game_data": {
"answer": "([{({{{[(([({({{{{{[]()[]}[][]()}()}[]}[]})}[])]))]}}})}])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 20,
"full_sequence": "([{({{{[(([({({{{{{[]()[]}[][]()}()}[]}[]})}[])]))]}}})}])",
"n_types": 3,
"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 y... | {
"game_data": {
"answer": "{⟨{(<⟨⟨⟨((<⟨<()<>{}>⟩>))<>⟩⟩⟩>[][]())}{}⟨⟩⟩}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "{⟨{(<⟨⟨⟨((<⟨<()<>{}>⟩>))<>⟩⟩⟩>[][]())}{}⟨⟩⟩}",
"n_types": 5,
"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": 5,
"nesting_depth": 0,
"opening_prefix": "{[[",
"prompt_name": "fill_in",
"prompt_variant": 7,
... |
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 sequen... | {
"game_data": {
"answer": "[{({{⟦⦅⦃(<{⦃<⦅⦆()>⦄}>⦅⦆)⦅⦆(){}⦄⦅⦆⦆⟧}<>[]⟦⟧}⟨⟩)}]()<>[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "[{({{⟦⦅⦃(<{⦃<⦅⦆()>⦄}>⦅⦆)⦅⦆(){}⦄⦅⦆⦆⟧}<>[]⟦⟧}⟨⟩)}]()<>[]",
"n_types": 8,
"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": 12,
"full_sequence": "(⦃(⟦⦃⟨⦅⦃((<<>>))⦄⦆⟩⦄⟧{}())⦃⦄⦄⦃⦄)[]()⦅⦆⟦⟧⟦⟧⟨⟩⦅⦆()[]⦃⦄⟦⟧{}<>",
"n_types": 8,
"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": 7,
"full_sequence": "⦅(⦅[⟦⟨{⦃⦄⟦⟧}⟩⟧]⦆)<>⦆⦃⦄[]()⟦⟧<>{}⟦⟧⟦⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦅(⦅[⟦⟨{",
"prompt_na... |
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": 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": 8,
"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": 4,
"nesting_depth": 0,
"opening_prefix": "[{(<[",
"prompt_name": "fill_in",
"pro... |
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": 6,
"nesting_depth": 0,
"opening_prefix": "<{⟦[<⟦[",
"prompt_name": "fill_in",
"promp... |
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": 11,
"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": 15,
"full_sequence": "{[<⟨({[[<⟨{(⟨⟨{[]{}}⟩[]⟩{}{}<>)}⟨⟩⟩()>]]{}<>})⟩>]}",
"n_types": 5,
"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": 12,
"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) ... | {
"game_data": {
"answer": "[[{{[(<<(({[{<[(<[]()>)][]>()}]})<>())>>)][]<>}}]]<>(){}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"full_sequence": "[[{{[(<<(({[{<[(<[]()>)][]>()}]})<>())>>)][]<>}}]]<>(){}",
"n_types": 4,
"nesting_depth": 0,
"ope... |
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 back... | {
"game_data": {
"answer": "{⟨{[[⟨{⟨⟨(<⟨⟩<>>)[]()⟩⟩}⟩]⟨⟩]}<>⟩<>}⟨⟩()<>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "{⟨{[[⟨{⟨⟨(<⟨⟩<>>)[]()⟩⟩}⟩]⟨⟩]}<>⟩<>}⟨⟩()<>",
"n_types": 5,
"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": 2,
"full_sequence": "[({}())]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[(",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 142856259... |
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": 8,
"nesting_depth": 0,
"opening_prefix": "{<⟨",
"prompt_name": "story",
"prompt_variant": 4,
"... |
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": 5,
"nesting_depth": 0,
"opening_prefix": "{{(<{",
"prompt_name": "qa",
"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": 17,
"full_sequence": "⟨⟦[[⦃{<⦃{⟦{⟨⦃[{(⦃⦄)}{}][]⦄⟩}[]⟧}⦃⦄⦄<>>⟦⟧{}}⦄]]⟦⟧⟧⟩",
"n_types": 7,
"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": 13,
"full_sequence": "⟨⟦(⦃<⟨(⦃[<⟦(⟨()⟩)⟧⟨⟩⦃⦄>]()⦄)⟨⟩⟨⟩⟩>⦄<>{})()⟧⟩⟨⟩⦃⦄⟦⟧",
"n_types": 7,
"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": 9,
"full_sequence": "⟨<[<⦃⦃⟦⟨<⟦⟧()>⟩⟧⦄⦄>]>()⟩()<>{}⦃⦄",
"n_types": 7,
"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 backti... | {
"game_data": {
"answer": "⟨⟨{[⟦[⟦⟨(<((())()<>)>)<>{}⟩[]⟧]⟧⟨⟩]}⟩⟩⦃⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "⟨⟨{[⟦[⟦⟨(<((())()<>)>)<>{}⟩[]⟧]⟧⟨⟩]}⟩⟩⦃⦄",
"n_types": 7,
"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... | {
"game_data": {
"answer": "[([{(<{(([{[]}])()<><>)}()>)}()])][]{}()<>{}[]{}[][]()<>{}{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "[([{(<{(([{[]}])()<><>)}()>)}()])][]{}()<>{}[]{}[][]()<>{}{}",
"n_types": 4,
"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": 10,
"full_sequence": "<<{<[<<<(⟨⟩)>>>]>}>>(){}⟦⟧{}()",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<{<[<<<(⟨",
"prompt_name": "qa... |
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... |
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": 7,
"nesting_depth": 0,
"opening_prefix": "⟨(",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 108533... |
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": 10,
"full_sequence": "([[[((([[{[]}{}[]]])){})]]]){}[][]",
"n_types": 3,
"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 yo... | {
"game_data": {
"answer": "{{([⟨[(⟨⟨⟨⟨⟨<⟨[{[()]}⟨⟩][]⟩[]>⟩⟩⟩[]⟩⟩)()]⟩])}}()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 18,
"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... | {
"game_data": {
"answer": "⟨⟦⟦(({{({⟦⟧⟦⟧(){}})}}))⦃⦄⟧<>⦃⦄⟧[]⟩{}⟨⟩⦃⦄⟦⟧⟦⟧()⟨⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"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": 16,
"full_sequence": "({(({[[([[{[{{[{}][][][]}[]}]{}[]}{}]]{})]]()}))[]})",
"n_types": 3,
"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 sequence) in... | {
"game_data": {
"answer": "<⟦[[[⟨<⟨{(<>)}<>⟩{}⟨⟩{}><>⟩<>{}<>]]]⟧><>[]{}[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"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": 1,
"full_sequence": "([]){}",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 1652... |
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 bra... | {
"game_data": {
"answer": "{{[(<⟨{}⟨⟩⟩>())]()⟨⟩}}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "{{[(<⟨{}⟨⟩⟩>())]()⟨⟩}}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{{[(<⟨",
"prompt_name": "direct",
"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": 6,
"full_sequence": "{[<{⟨[]()⟩}⟨⟩>]}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{[<{⟨[",
"prompt_name": "mathematical",
"prompt_varian... |
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 pair... | {
"game_data": {
"answer": "<(<⟦()⟧>[])>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "<(<⟦()⟧>[])>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<(<⟦(",
"prompt_name": "direct",
"prompt_variant": 0,
"s... |
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": 17,
"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 sequence) in b... | {
"game_data": {
"answer": "<⟦{⟦[(⟦⟦<(([{⟨[{<{⟦⟧}><>}]⟩}][])⟨⟩)>⟧⟧){}]⟧{}<>}⟧()>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 19,
"full_sequence": "<⟦{⟦[(⟦⟦<(([{⟨[{<{⟦⟧}><>}]⟩}][])⟨⟩)>⟧⟧){}]⟧{}<>}⟧()>",
"n_types": 6,
"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": 2,
"full_sequence": "(()[])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "((",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 191738... |
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": 18,
"full_sequence": "[{{<<[((<<<{[[{<{<>}>()}]][]}()>{}(){}><>>))]>>}}]",
"n_types": 4,
"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": 6,
"full_sequence": "[[<{<{}>()}[]{}>]]",
"n_types": 4,
"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 provide ... | {
"game_data": {
"answer": "{{([((<{<<{{[[[]]]}}>>}><>()())<>()<>⟨⟩<>)])}}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 14,
"full_sequence": "{{([((<{<<{{[[[]]]}}>>}><>()())<>()<>⟨⟩<>)])}}",
"n_types": 5,
"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": 2,
"full_sequence": "{([]⟨⟩)}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{(",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 13... |
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": 10,
"full_sequence": "([{[{{{(({{}}){})}}}]}]){}[]",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([{[{{{(({",
"prompt_name": "puzzle... |
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": 3,
"nesting_depth": 0,
"opening_prefix": "([({[([[[",
"prompt_name": "... |
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": 7,
"full_sequence": "[{[{({{}}{})}]}<>][][]()",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{[{({{",
"prompt_name": "story",
"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 backti... | {
"game_data": {
"answer": "<⟦{{⟨[⟨((<⟦(⟨(([{<⟦<⟨⟩>⟧()⟨⟩>}⟨⟩()]))⟩)⟧>))⟩]⟩}}⟧>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 20,
"full_sequence": "<⟦{{⟨[⟨((<⟦(⟨(([{<⟦<⟨⟩>⟧()⟨⟩>}⟨⟩()]))⟩)⟧>))⟩]⟩}}⟧>",
"n_types": 6,
"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": 5,
"full_sequence": "⟨(⦃<⟨⟩>⦄⦃⦄)⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨(⦃<⟨",
"prompt_name": "puzzle",
"prompt_variant": 2,
"s... |
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": 2,
"full_sequence": "[[][]]<>[]<><>",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[[",
"prompt_name": "puzzle",
"prompt_variant": 2,
"... |
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... | {
"game_data": {
"answer": "((([({([{({}{}())[]}]){}})])()))()[]()[]()[]()[]{}{}()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "((([({([{({}{}())[]}]){}})])()))()[]()[]()[]()[]{}{}()",
"n_types": 3,
"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": 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": 1,
"full_sequence": "<⟦⟧><>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 116074693... |
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": 14,
"full_sequence": "{{[⟦⦃([<⟦⦃⦅{⟨⦃⦄⟩}⦆⦄⟧⦅⦆⟦⟧>⦃⦄])⦄⟧[]⟦⟧()⦅⦆]}}<>⦃⦄⟨⟩<><>",
"n_types": 8,
"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) i... | {
"game_data": {
"answer": "<⟦({((⟨({<<⟨⟩>>⟦⟧})[]⟦⟧⟩⟦⟧<>))}()<>)⟧()><>⟨⟩⟨⟩()⟦⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "<⟦({((⟨({<<⟨⟩>>⟦⟧})[]⟦⟧⟩⟦⟧<>))}()<>)⟧()><>⟨⟩⟨⟩()⟦⟧",
"n_types": 6,
"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 ... | {
"game_data": {
"answer": "⦃⟨⟦[[[{[⟨[{{(⟦⟦⟦⟧⟧⟧⟦⟧⟦⟧⦃⦄)}}]⦃⦄⟨⟩⟩]}[]⟨⟩]]⟦⟧[]]⟧⟩⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 16,
"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": 21,
"full_sequence": "[<{[[((({{{<(([<<<((<><>{}))>>>]))>}}})))]]}>]",
"n_types": 4,
"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 seque... | {
"game_data": {
"answer": "(⟨[((⟦<⟦⟨⟦(⦅⦆)⟨⟩⟧()()⦃⦄⟩⟦⟧⟧>⟧)<>)<><>⦅⦆]⟨⟩⟩()⦃⦄)⟨⟩⦅⦆⦅⦆{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "(⟨[((⟦<⟦⟨⟦(⦅⦆)⟨⟩⟧()()⦃⦄⟩⟦⟧⟧>⟧)<>)<><>⦅⦆]⟨⟩⟩()⦃⦄)⟨⟩⦅⦆⦅⦆{}",
"n_types": 8,
"nesting_depth": 0,
"ope... |
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": 10,
"full_sequence": "⦅⟨{<<<⦃⦃⦅{{}⟨⟩{}}⦆⦄⦄[]>>>{}}⟩⦆<><>",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦅⟨{<<<⦃⦃⦅{",
"prompt_na... |
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": 6,
"full_sequence": "[[<({[[]]})>]]<>[]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[[<({[",
"prompt_name": "direct",
"prompt_variant"... |
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": 7,
"full_sequence": "⦅(<{[<[]>[]]}<>>)⦆[]⟦⟧⟨⟩⟦⟧{}⦃⦄<><>()",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦅(<{[<[",
"prompt_na... |
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": 22,
"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": 14,
"full_sequence": "⟨⟨<⟦{[⟨[<<<⦃{()⟨⟩}⦄>>><>]⟩()⦃⦄]}()⟧>⟩⟩",
"n_types": 7,
"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": 11,
"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 seq... | {
"game_data": {
"answer": "[([<<{{{<<<(<<>()>)>>>{}{}}<>}}[]()()()<>{}[]>>{}()<>[]])]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 14,
"full_sequence": "[([<<{{{<<<(<<>()>)>>>{}{}}<>}}[]()()()<>{}[]>>{}()<>[]])]",
"n_types": 4,
"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 `an... | {
"game_data": {
"answer": "<<⟦[{⟨<<<⟨<⟦[⟦[[]]⟧]⟧>⟩>>>⟩}]⟧>>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 16,
"full_sequence": "<<⟦[{⟨<<<⟨<⟦[⟦[[]]⟧]⟧>⟩>>>⟩}]⟧>>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<⟦[{⟨<<<⟨<⟦[⟦[[",
"prompt_... |
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": 13,
"full_sequence": "<⟦⟨⟦[⟦⟦(<[<{⟦⟧}<>⟨⟩>()⟨⟩]⟨⟩[]>)⟧⟧]⟧⟩[]⟦⟧⟧>[]⟨⟩⟦⟧",
"n_types": 6,
"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": 6,
"full_sequence": "<{[⟨⟦{[]⟨⟩}⟧⟩]}>⟨⟩⟨⟩<>[]",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{[⟨⟦{",
"prompt_name": "story",
"prom... |
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": 11,
"full_sequence": "[{<<([({{[<{}>]()}})])>>}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{<<([({{[<",
"prompt_name": "qa",
... |
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": 9,
"full_sequence": "⟦⟨{⦃⦃⟨(⟨()⟩)⟩⦄⦄<>}⟩⟧<>⟦⟧⦃⦄⟦⟧",
"n_types": 8,
"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": 20,
"full_sequence": "<⟨{⟨⟨<({⟦⟨([(⟦<{[{{⟦⟧}}]}>()⟧)]{})⟩⟧})>⟩⟩}⟩>",
"n_types": 6,
"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 comp... | {
"game_data": {
"answer": "(⦃⦄)⦅⦆",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 1,
"full_sequence": "(⦃⦄)⦅⦆",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "(",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"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": 19,
"full_sequence": "{[{{(({⟨({{[(⟨{{⟨⟨⟨⟨⟩{}⟨⟩{}⟩⟩⟨⟩⟩[]<>}}<>()⟩)[]]}})⟩}){})}}]}",
"n_types": 5,
"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 yo... | {
"game_data": {
"answer": "<⟨[(⟦<<({⟨⟩⟦⟧}⟦⟧⟦⟧[])>>⟧)]⟩>{}[]⟨⟩()⟦⟧⟨⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "<⟨[(⟦<<({⟨⟩⟦⟧}⟦⟧⟦⟧[])>>⟧)]⟩>{}[]⟨⟩()⟦⟧⟨⟩",
"n_types": 6,
"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": 2,
"full_sequence": "<({})<>>⟨⟩",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<(",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 14... |
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": 7,
"nesting_depth": 0,
"opening_prefix": "⟨(⟨",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 17... |
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