data_type stringclasses 6
values | problem stringlengths 928 3.45k | solution stringclasses 2
values | verification stringlengths 177 1.97k ⌀ |
|---|---|---|---|
sudoku_lookahead | You are given a partially filled 9x9 Sudoku grid represented as a list of lists, where empty cells are represented as 0. Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if it's possible to fill the remaining cells according to standard... | (B) | null |
game24_lookahead | You are given four numbers and the current calculation state for the Game of 24.
Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if the remaining numbers can be combined using basic arithmetic operations (+ - * /) to reach exactly 24. ... | (A) | null |
game24_lookahead | You are given four numbers and the current calculation state for the Game of 24.
Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if the remaining numbers can be combined using basic arithmetic operations (+ - * /) to reach exactly 24. ... | (A) | null |
sudoku_lookahead | You are given a partially filled 9x9 Sudoku grid represented as a list of lists, where empty cells are represented as 0. Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if it's possible to fill the remaining cells according to standard... | (B) | null |
sudoku_lookahead | You are given a partially filled 9x9 Sudoku grid represented as a list of lists, where empty cells are represented as 0. Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if it's possible to fill the remaining cells according to standard... | (A) | null |
game24_statetransition | You are given an initial Game of 24 configuration S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid solu... | null | {'parent_state': ['1', '1', '5', '8'], 'current_state': ['(1 + 1)', '5', '8'], 'current_status': 'Solvable', 'unsolvable_child': ['((1 + 1) + 5)', '8'], 'numbers': [1, 1, 5, 8]} |
sudoku_statetransition | You are given an initial Sudoku puzzle S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid Sudoku solution... | null | {'parent_state': [[7, 5, 9, 8, 3, 1, 6, 2, 4], [8, 6, 1, 4, 7, 2, 9, 5, 3], [4, 3, 2, 9, 6, 5, 8, 7, 1], [1, 7, 6, 5, 4, 8, 2, 3, 9], [9, 4, 3, 1, 2, 7, 5, 8, 6], [2, 8, 5, 3, 9, 6, 1, 4, 7], [3, 0, 8, 7, 0, 0, 0, 6, 0], [0, 0, 4, 2, 8, 3, 0, 0, 5], [0, 2, 7, 6, 0, 0, 3, 9, 0]], 'current_state': [[7, 5, 9, 8, 3, 1, 6, ... |
sudoku_statetransition | You are given an initial Sudoku puzzle S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid Sudoku solution... | null | {'parent_state': [[5, 7, 4, 8, 3, 9, 2, 1, 6], [8, 2, 3, 1, 6, 5, 7, 9, 4], [6, 1, 9, 2, 4, 7, 5, 8, 3], [4, 9, 6, 3, 5, 8, 1, 2, 7], [2, 0, 1, 4, 0, 6, 0, 0, 9], [3, 0, 0, 0, 1, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 9, 5, 1], [0, 6, 0, 0, 9, 3, 0, 0, 8], [0, 0, 0, 7, 8, 1, 0, 0, 0]], 'current_state': [[5, 7, 4, 8, 3, 9, 2, ... |
graphcoloring_lookahead | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given the current coloring state of the graph in a list, where each index represents the corresonding vertex, and the number at that index represent... | (B) | null |
game24_lookahead | You are given four numbers and the current calculation state for the Game of 24.
Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if the remaining numbers can be combined using basic arithmetic operations (+ - * /) to reach exactly 24. ... | (B) | null |
sudoku_lookahead | You are given a partially filled 9x9 Sudoku grid represented as a list of lists, where empty cells are represented as 0. Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if it's possible to fill the remaining cells according to standard... | (B) | null |
sudoku_statetransition | You are given an initial Sudoku puzzle S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid Sudoku solution... | null | {'parent_state': [[9, 1, 3, 7, 0, 0, 8, 0, 2], [0, 8, 0, 0, 3, 0, 0, 0, 6], [2, 7, 0, 0, 0, 0, 0, 1, 0], [0, 0, 4, 9, 0, 3, 5, 0, 0], [0, 0, 0, 2, 0, 1, 6, 8, 4], [5, 0, 1, 0, 8, 0, 0, 7, 0], [0, 0, 2, 4, 6, 0, 0, 0, 8], [1, 0, 0, 0, 0, 5, 9, 0, 0], [0, 3, 9, 8, 0, 0, 0, 4, 0]], 'current_state': [[9, 1, 3, 7, 5, 0, 8, ... |
sudoku_lookahead | You are given a partially filled 9x9 Sudoku grid represented as a list of lists, where empty cells are represented as 0. Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if it's possible to fill the remaining cells according to standard... | (B) | null |
game24_lookahead | You are given four numbers and the current calculation state for the Game of 24.
Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if the remaining numbers can be combined using basic arithmetic operations (+ - * /) to reach exactly 24. ... | (B) | null |
sudoku_lookahead | You are given a partially filled 9x9 Sudoku grid represented as a list of lists, where empty cells are represented as 0. Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if it's possible to fill the remaining cells according to standard... | (A) | null |
game24_lookahead | You are given four numbers and the current calculation state for the Game of 24.
Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if the remaining numbers can be combined using basic arithmetic operations (+ - * /) to reach exactly 24. ... | (A) | null |
game24_lookahead | You are given four numbers and the current calculation state for the Game of 24.
Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if the remaining numbers can be combined using basic arithmetic operations (+ - * /) to reach exactly 24. ... | (B) | null |
graphcoloring_lookahead | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given the current coloring state of the graph in a list, where each index represents the corresonding vertex, and the number at that index represent... | (A) | null |
game24_statetransition | You are given an initial Game of 24 configuration S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid solu... | null | {'parent_state': ['1', '5', '6', '12'], 'current_state': ['(1 * 6)', '5', '12'], 'current_status': 'Unsolvable', 'unsolvable_child': ['((1 * 6) + 5)', '12'], 'numbers': [1, 5, 6, 12]} |
game24_statetransition | You are given an initial Game of 24 configuration S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid solu... | null | {'parent_state': ['1', '1', '4', '9'], 'current_state': ['(1 + 4)', '1', '9'], 'current_status': 'Unsolvable', 'unsolvable_child': ['((1 + 4) + 1)', '9'], 'numbers': [1, 1, 4, 9]} |
graphcoloring_statetransition | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given a sequence of partial coloring states leading to the current coloring state S(i). The coloring state is a list, where each index represents th... | null | {'parent_state': [1, 2, 1, 1, 3, 2, 1, 3, 2, 4, 5, 4, 6, 4, 7, 3, 6, 5, 2, 5, 0, 0, 0, 0], 'current_state': [1, 2, 1, 1, 3, 2, 1, 3, 2, 4, 5, 4, 6, 4, 7, 3, 6, 5, 2, 5, 5, 0, 0, 0], 'current_status': 'Solvable', 'unsolvable_child': [1, 2, 1, 1, 3, 2, 1, 3, 2, 4, 5, 4, 6, 4, 7, 3, 6, 5, 2, 5, 5, 8, 0, 0], 'graph': [[1, ... |
graphcoloring_statetransition | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given a sequence of partial coloring states leading to the current coloring state S(i). The coloring state is a list, where each index represents th... | null | {'parent_state': [1, 2, 1, 3, 4, 2, 1, 2, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'current_state': [1, 2, 1, 3, 4, 2, 1, 2, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'current_status': 'Solvable', 'unsolvable_child': [1, 2, 1, 3, 4, 2, 1, 2, 5, 1, 6, 0, 0, 0, 0, 0, 0, 0], 'graph': [[1, 8, 11, 13, 16, 17], [0, 2, 3, 4, 6, 9, 11, 12, 15, 16,... |
game24_lookahead | You are given four numbers and the current calculation state for the Game of 24.
Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if the remaining numbers can be combined using basic arithmetic operations (+ - * /) to reach exactly 24. ... | (B) | null |
game24_lookahead | You are given four numbers and the current calculation state for the Game of 24.
Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if the remaining numbers can be combined using basic arithmetic operations (+ - * /) to reach exactly 24. ... | (B) | null |
graphcoloring_lookahead | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given the current coloring state of the graph in a list, where each index represents the corresonding vertex, and the number at that index represent... | (B) | null |
sudoku_lookahead | You are given a partially filled 9x9 Sudoku grid represented as a list of lists, where empty cells are represented as 0. Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if it's possible to fill the remaining cells according to standard... | (A) | null |
sudoku_statetransition | You are given an initial Sudoku puzzle S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid Sudoku solution... | null | {'parent_state': [[6, 2, 4, 7, 5, 3, 1, 9, 8], [1, 8, 7, 9, 4, 6, 5, 2, 3], [5, 3, 9, 8, 2, 1, 4, 6, 7], [2, 0, 5, 3, 6, 0, 7, 0, 0], [0, 0, 0, 0, 7, 5, 9, 0, 2], [0, 1, 3, 0, 0, 0, 0, 0, 0], [9, 7, 6, 0, 0, 2, 0, 8, 5], [0, 0, 1, 0, 0, 0, 0, 4, 0], [8, 4, 0, 0, 3, 0, 0, 0, 1]], 'current_state': [[6, 2, 4, 7, 5, 3, 1, ... |
graphcoloring_lookahead | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given the current coloring state of the graph in a list, where each index represents the corresonding vertex, and the number at that index represent... | (A) | null |
game24_lookahead | You are given four numbers and the current calculation state for the Game of 24.
Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if the remaining numbers can be combined using basic arithmetic operations (+ - * /) to reach exactly 24. ... | (B) | null |
sudoku_statetransition | You are given an initial Sudoku puzzle S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid Sudoku solution... | null | {'parent_state': [[7, 6, 3, 5, 2, 8, 9, 1, 4], [9, 8, 4, 7, 3, 1, 2, 5, 6], [1, 2, 5, 6, 9, 4, 3, 8, 7], [4, 5, 8, 2, 6, 9, 7, 3, 1], [6, 3, 1, 8, 0, 7, 5, 0, 0], [2, 9, 0, 0, 0, 0, 0, 0, 8], [5, 0, 2, 4, 0, 0, 0, 0, 0], [0, 7, 0, 3, 1, 0, 0, 6, 5], [0, 0, 6, 0, 8, 0, 1, 7, 0]], 'current_state': [[7, 6, 3, 5, 2, 8, 9, ... |
sudoku_statetransition | You are given an initial Sudoku puzzle S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid Sudoku solution... | null | {'parent_state': [[5, 3, 6, 1, 9, 2, 8, 4, 7], [4, 1, 7, 8, 3, 0, 0, 0, 0], [8, 0, 9, 0, 0, 5, 0, 3, 1], [0, 0, 2, 0, 0, 0, 0, 8, 3], [0, 0, 0, 6, 4, 0, 0, 7, 5], [3, 7, 0, 0, 1, 8, 9, 0, 0], [0, 5, 0, 7, 6, 9, 0, 0, 0], [7, 0, 4, 0, 8, 0, 0, 2, 0], [1, 0, 0, 3, 0, 0, 0, 5, 9]], 'current_state': [[5, 3, 6, 1, 9, 2, 8, ... |
graphcoloring_statetransition | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given a sequence of partial coloring states leading to the current coloring state S(i). The coloring state is a list, where each index represents th... | null | {'parent_state': [1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'current_state': [1, 2, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'current_status': 'Solvable', 'unsolvable_child': [1, 2, 2, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'grap... |
sudoku_statetransition | You are given an initial Sudoku puzzle S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid Sudoku solution... | null | {'parent_state': [[1, 9, 7, 2, 8, 6, 5, 3, 4], [5, 4, 8, 1, 9, 3, 7, 6, 2], [6, 3, 2, 7, 4, 5, 9, 8, 1], [2, 8, 4, 3, 1, 7, 6, 5, 9], [9, 6, 1, 5, 2, 8, 4, 7, 3], [7, 5, 3, 4, 6, 9, 2, 1, 8], [3, 1, 0, 6, 5, 0, 0, 0, 0], [0, 0, 0, 9, 0, 0, 1, 2, 6], [0, 2, 0, 0, 7, 0, 0, 9, 0]], 'current_state': [[1, 9, 7, 2, 8, 6, 5, ... |
sudoku_lookahead | You are given a partially filled 9x9 Sudoku grid represented as a list of lists, where empty cells are represented as 0. Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if it's possible to fill the remaining cells according to standard... | (B) | null |
game24_statetransition | You are given an initial Game of 24 configuration S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid solu... | null | {'parent_state': ['1', '5', '5', '13'], 'current_state': ['(5 * 13)', '1', '5'], 'current_status': 'Unsolvable', 'unsolvable_child': ['((5 * 13) + 1)', '5'], 'numbers': [1, 5, 5, 13]} |
graphcoloring_statetransition | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given a sequence of partial coloring states leading to the current coloring state S(i). The coloring state is a list, where each index represents th... | null | {'parent_state': [1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'current_state': [1, 1, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'current_status': 'Solvable', 'unsolvable_child': [1, 1, 2, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'graph': [[2, ... |
sudoku_lookahead | You are given a partially filled 9x9 Sudoku grid represented as a list of lists, where empty cells are represented as 0. Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if it's possible to fill the remaining cells according to standard... | (B) | null |
game24_statetransition | You are given an initial Game of 24 configuration S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid solu... | null | {'parent_state': ['3', '3', '3', '9'], 'current_state': ['(3 / 3)', '3', '9'], 'current_status': 'Solvable', 'unsolvable_child': ['((3 / 3) + 3)', '9'], 'numbers': [3, 3, 3, 9]} |
game24_statetransition | You are given an initial Game of 24 configuration S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid solu... | null | {'parent_state': ['4', '4', '4', '12'], 'current_state': ['(12 - 4)', '4', '4'], 'current_status': 'Solvable', 'unsolvable_child': ['((12 - 4) + 4)', '4'], 'numbers': [4, 4, 4, 12]} |
graphcoloring_statetransition | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given a sequence of partial coloring states leading to the current coloring state S(i). The coloring state is a list, where each index represents th... | null | {'parent_state': [1, 2, 1, 3, 4, 3, 3, 1, 4, 5, 2, 5, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'current_state': [1, 2, 1, 3, 4, 3, 3, 1, 4, 5, 2, 5, 6, 7, 0, 0, 0, 0, 0, 0, 0, 0], 'current_status': 'Unsolvable', 'unsolvable_child': [1, 2, 1, 3, 4, 3, 3, 1, 4, 5, 2, 5, 6, 7, 6, 0, 0, 0, 0, 0, 0, 0], 'graph': [[1, 3, 4, 5, 6, 9, 1... |
sudoku_statetransition | You are given an initial Sudoku puzzle S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid Sudoku solution... | null | {'parent_state': [[6, 4, 5, 3, 1, 7, 2, 9, 8], [9, 3, 2, 8, 4, 6, 7, 5, 1], [8, 7, 1, 5, 2, 9, 4, 6, 3], [2, 9, 6, 1, 8, 4, 5, 3, 7], [3, 1, 7, 9, 5, 2, 8, 4, 6], [4, 5, 8, 7, 6, 3, 1, 0, 9], [0, 0, 0, 0, 9, 0, 3, 1, 0], [0, 6, 0, 0, 7, 0, 9, 0, 2], [1, 8, 0, 0, 3, 5, 0, 0, 4]], 'current_state': [[6, 4, 5, 3, 1, 7, 2, ... |
game24_lookahead | You are given four numbers and the current calculation state for the Game of 24.
Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if the remaining numbers can be combined using basic arithmetic operations (+ - * /) to reach exactly 24. ... | (A) | null |
sudoku_statetransition | You are given an initial Sudoku puzzle S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid Sudoku solution... | null | {'parent_state': [[9, 3, 8, 7, 2, 1, 4, 5, 6], [7, 1, 6, 5, 4, 8, 9, 3, 2], [2, 4, 5, 9, 6, 3, 1, 8, 7], [5, 7, 9, 4, 3, 6, 2, 1, 8], [4, 2, 1, 8, 9, 5, 6, 7, 3], [6, 8, 3, 1, 7, 2, 5, 9, 4], [0, 0, 7, 0, 0, 0, 3, 4, 0], [3, 0, 0, 6, 0, 7, 0, 0, 5], [0, 0, 2, 0, 8, 0, 0, 0, 9]], 'current_state': [[9, 3, 8, 7, 2, 1, 4, ... |
game24_lookahead | You are given four numbers and the current calculation state for the Game of 24.
Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if the remaining numbers can be combined using basic arithmetic operations (+ - * /) to reach exactly 24. ... | (B) | null |
sudoku_lookahead | You are given a partially filled 9x9 Sudoku grid represented as a list of lists, where empty cells are represented as 0. Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if it's possible to fill the remaining cells according to standard... | (B) | null |
game24_statetransition | You are given an initial Game of 24 configuration S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid solu... | null | {'parent_state': ['8', '8', '8', '13'], 'current_state': ['(8 / 8)', '8', '13'], 'current_status': 'Unsolvable', 'unsolvable_child': ['((8 / 8) + 8)', '13'], 'numbers': [8, 8, 8, 13]} |
graphcoloring_lookahead | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given the current coloring state of the graph in a list, where each index represents the corresonding vertex, and the number at that index represent... | (B) | null |
game24_statetransition | You are given an initial Game of 24 configuration S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid solu... | null | {'parent_state': ['9', '10', '11', '12'], 'current_state': ['(11 - 10)', '9', '12'], 'current_status': 'Unsolvable', 'unsolvable_child': ['((11 - 10) + 9)', '12'], 'numbers': [9, 10, 11, 12]} |
sudoku_statetransition | You are given an initial Sudoku puzzle S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid Sudoku solution... | null | {'parent_state': [[8, 6, 5, 3, 1, 4, 9, 7, 2], [9, 1, 2, 7, 8, 5, 6, 4, 3], [3, 7, 4, 9, 6, 2, 8, 1, 5], [5, 3, 9, 1, 2, 8, 7, 6, 4], [6, 4, 1, 5, 9, 7, 3, 2, 8], [7, 2, 8, 6, 4, 3, 5, 9, 1], [2, 9, 7, 8, 5, 1, 4, 3, 6], [4, 5, 0, 0, 7, 0, 0, 0, 9], [1, 0, 0, 4, 0, 9, 0, 0, 0]], 'current_state': [[8, 6, 5, 3, 1, 4, 9, ... |
game24_statetransition | You are given an initial Game of 24 configuration S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid solu... | null | {'parent_state': ['2', '2', '5', '11'], 'current_state': ['(5 - 2)', '2', '11'], 'current_status': 'Unsolvable', 'unsolvable_child': ['((5 - 2) + 2)', '11'], 'numbers': [2, 2, 5, 11]} |
game24_statetransition | You are given an initial Game of 24 configuration S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid solu... | null | {'parent_state': ['3', '4', '10', '13'], 'current_state': ['(10 + 13)', '3', '4'], 'current_status': 'Solvable', 'unsolvable_child': ['((10 + 13) + 3)', '4'], 'numbers': [3, 4, 10, 13]} |
sudoku_statetransition | You are given an initial Sudoku puzzle S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid Sudoku solution... | null | {'parent_state': [[5, 8, 4, 1, 9, 6, 3, 7, 2], [7, 2, 3, 8, 4, 5, 6, 9, 1], [9, 6, 1, 2, 3, 7, 8, 4, 5], [4, 1, 5, 6, 7, 3, 2, 8, 9], [2, 9, 6, 5, 8, 4, 1, 3, 7], [3, 7, 8, 9, 1, 2, 5, 6, 4], [1, 4, 7, 3, 5, 8, 9, 2, 0], [6, 0, 0, 0, 0, 1, 0, 0, 8], [8, 0, 2, 4, 0, 9, 0, 1, 0]], 'current_state': [[5, 8, 4, 1, 9, 6, 3, ... |
sudoku_statetransition | You are given an initial Sudoku puzzle S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid Sudoku solution... | null | {'parent_state': [[6, 7, 3, 5, 2, 1, 4, 8, 9], [9, 1, 4, 6, 3, 8, 2, 7, 5], [8, 2, 5, 7, 4, 9, 6, 1, 3], [7, 6, 1, 3, 8, 5, 9, 2, 4], [4, 3, 8, 2, 9, 7, 1, 5, 6], [0, 0, 0, 4, 0, 6, 8, 0, 0], [0, 4, 9, 0, 5, 3, 0, 0, 0], [0, 0, 0, 1, 0, 0, 3, 0, 8], [0, 0, 0, 0, 7, 2, 0, 4, 1]], 'current_state': [[6, 7, 3, 5, 2, 1, 4, ... |
graphcoloring_lookahead | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given the current coloring state of the graph in a list, where each index represents the corresonding vertex, and the number at that index represent... | (A) | null |
graphcoloring_statetransition | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given a sequence of partial coloring states leading to the current coloring state S(i). The coloring state is a list, where each index represents th... | null | {'parent_state': [1, 2, 3, 1, 4, 2, 3, 5, 5, 6, 6, 7, 4, 1, 7, 8, 9, 10, 10, 0, 0, 0, 0], 'current_state': [1, 2, 3, 1, 4, 2, 3, 5, 5, 6, 6, 7, 4, 1, 7, 8, 9, 10, 10, 11, 0, 0, 0], 'current_status': 'Solvable', 'unsolvable_child': [1, 2, 3, 1, 4, 2, 3, 5, 5, 6, 6, 7, 4, 1, 7, 8, 9, 10, 10, 11, 12, 0, 0], 'graph': [[1, ... |
graphcoloring_statetransition | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given a sequence of partial coloring states leading to the current coloring state S(i). The coloring state is a list, where each index represents th... | null | {'parent_state': [1, 2, 1, 2, 2, 3, 3, 4, 2, 1, 4, 5, 0, 0, 0], 'current_state': [1, 2, 1, 2, 2, 3, 3, 4, 2, 1, 4, 5, 5, 0, 0], 'current_status': 'Solvable', 'unsolvable_child': [1, 2, 1, 2, 2, 3, 3, 4, 2, 1, 4, 5, 5, 5, 0], 'graph': [[1, 5, 6, 10, 12, 13], [0, 2, 7, 10, 11, 12, 14], [1, 3, 4, 7, 12, 13], [2, 5, 7, 10,... |
sudoku_lookahead | You are given a partially filled 9x9 Sudoku grid represented as a list of lists, where empty cells are represented as 0. Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if it's possible to fill the remaining cells according to standard... | (A) | null |
graphcoloring_statetransition | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given a sequence of partial coloring states leading to the current coloring state S(i). The coloring state is a list, where each index represents th... | null | {'parent_state': [1, 2, 3, 1, 4, 2, 3, 5, 5, 6, 6, 7, 4, 1, 7, 8, 9, 10, 0, 0, 0, 0, 0], 'current_state': [1, 2, 3, 1, 4, 2, 3, 5, 5, 6, 6, 7, 4, 1, 7, 8, 9, 10, 11, 0, 0, 0, 0], 'current_status': 'Unsolvable', 'unsolvable_child': [1, 2, 3, 1, 4, 2, 3, 5, 5, 6, 6, 7, 4, 1, 7, 8, 9, 10, 11, 12, 0, 0, 0], 'graph': [[1, 2... |
game24_statetransition | You are given an initial Game of 24 configuration S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid solu... | null | {'parent_state': ['3', '7', '7', '8'], 'current_state': ['(3 * 7)', '7', '8'], 'current_status': 'Solvable', 'unsolvable_child': ['((3 * 7) + 7)', '8'], 'numbers': [3, 7, 7, 8]} |
graphcoloring_lookahead | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given the current coloring state of the graph in a list, where each index represents the corresonding vertex, and the number at that index represent... | (B) | null |
game24_lookahead | You are given four numbers and the current calculation state for the Game of 24.
Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if the remaining numbers can be combined using basic arithmetic operations (+ - * /) to reach exactly 24. ... | (B) | null |
game24_lookahead | You are given four numbers and the current calculation state for the Game of 24.
Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if the remaining numbers can be combined using basic arithmetic operations (+ - * /) to reach exactly 24. ... | (A) | null |
sudoku_statetransition | You are given an initial Sudoku puzzle S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid Sudoku solution... | null | {'parent_state': [[9, 1, 3, 7, 8, 4, 5, 6, 2], [7, 6, 4, 3, 2, 5, 9, 1, 8], [8, 5, 2, 6, 1, 9, 4, 3, 7], [2, 4, 6, 8, 5, 3, 7, 9, 1], [1, 7, 8, 9, 6, 2, 3, 4, 5], [3, 9, 5, 4, 7, 1, 8, 2, 6], [5, 8, 0, 0, 4, 6, 0, 0, 0], [0, 0, 0, 1, 0, 0, 2, 5, 0], [4, 2, 0, 0, 3, 7, 0, 0, 9]], 'current_state': [[9, 1, 3, 7, 8, 4, 5, ... |
sudoku_lookahead | You are given a partially filled 9x9 Sudoku grid represented as a list of lists, where empty cells are represented as 0. Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if it's possible to fill the remaining cells according to standard... | (A) | null |
graphcoloring_lookahead | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given the current coloring state of the graph in a list, where each index represents the corresonding vertex, and the number at that index represent... | (A) | null |
graphcoloring_lookahead | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given the current coloring state of the graph in a list, where each index represents the corresonding vertex, and the number at that index represent... | (B) | null |
graphcoloring_lookahead | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given the current coloring state of the graph in a list, where each index represents the corresonding vertex, and the number at that index represent... | (A) | null |
sudoku_statetransition | You are given an initial Sudoku puzzle S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid Sudoku solution... | null | {'parent_state': [[3, 1, 2, 6, 5, 9, 8, 7, 4], [9, 8, 4, 2, 3, 7, 5, 1, 6], [5, 6, 7, 8, 4, 1, 2, 9, 3], [8, 2, 6, 1, 9, 3, 4, 5, 7], [4, 3, 5, 7, 6, 8, 9, 2, 1], [7, 9, 1, 4, 2, 5, 3, 6, 8], [1, 5, 9, 3, 7, 4, 6, 8, 2], [0, 0, 0, 0, 1, 2, 0, 3, 9], [0, 0, 3, 0, 8, 6, 0, 0, 0]], 'current_state': [[3, 1, 2, 6, 5, 9, 8, ... |
sudoku_lookahead | You are given a partially filled 9x9 Sudoku grid represented as a list of lists, where empty cells are represented as 0. Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if it's possible to fill the remaining cells according to standard... | (A) | null |
graphcoloring_statetransition | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given a sequence of partial coloring states leading to the current coloring state S(i). The coloring state is a list, where each index represents th... | null | {'parent_state': [1, 2, 1, 3, 3, 1, 4, 5, 1, 1, 2, 5, 4, 5, 6, 6, 4, 0, 0, 0, 0, 0], 'current_state': [1, 2, 1, 3, 3, 1, 4, 5, 1, 1, 2, 5, 4, 5, 6, 6, 4, 2, 0, 0, 0, 0], 'current_status': 'Unsolvable', 'unsolvable_child': [1, 2, 1, 3, 3, 1, 4, 5, 1, 1, 2, 5, 4, 5, 6, 6, 4, 2, 7, 0, 0, 0], 'graph': [[1, 4, 6, 10, 11, 12... |
game24_statetransition | You are given an initial Game of 24 configuration S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid solu... | null | {'parent_state': ['1', '1', '5', '5'], 'current_state': ['(1 * 5)', '1', '5'], 'current_status': 'Solvable', 'unsolvable_child': ['((1 * 5) + 1)', '5'], 'numbers': [1, 1, 5, 5]} |
graphcoloring_statetransition | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given a sequence of partial coloring states leading to the current coloring state S(i). The coloring state is a list, where each index represents th... | null | {'parent_state': [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'current_state': [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'current_status': 'Unsolvable', 'unsolvable_child': [1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'graph': [[3, 4, 7, 8, 9, 13, 15], [8, 10, 11, 13, 16], [6, 7, 10, 11], [0,... |
sudoku_lookahead | You are given a partially filled 9x9 Sudoku grid represented as a list of lists, where empty cells are represented as 0. Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if it's possible to fill the remaining cells according to standard... | (A) | null |
sudoku_lookahead | You are given a partially filled 9x9 Sudoku grid represented as a list of lists, where empty cells are represented as 0. Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if it's possible to fill the remaining cells according to standard... | (A) | null |
graphcoloring_statetransition | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given a sequence of partial coloring states leading to the current coloring state S(i). The coloring state is a list, where each index represents th... | null | {'parent_state': [1, 1, 2, 3, 4, 3, 2, 3, 5, 6, 1, 4, 5, 5, 6, 2, 7, 8, 9, 0, 0, 0, 0], 'current_state': [1, 1, 2, 3, 4, 3, 2, 3, 5, 6, 1, 4, 5, 5, 6, 2, 7, 8, 9, 7, 0, 0, 0], 'current_status': 'Unsolvable', 'unsolvable_child': [1, 1, 2, 3, 4, 3, 2, 3, 5, 6, 1, 4, 5, 5, 6, 2, 7, 8, 9, 7, 2, 0, 0], 'graph': [[3, 4, 5, 6... |
graphcoloring_lookahead | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given the current coloring state of the graph in a list, where each index represents the corresonding vertex, and the number at that index represent... | (B) | null |
game24_statetransition | You are given an initial Game of 24 configuration S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid solu... | null | {'parent_state': ['1', '8', '9', '11'], 'current_state': ['(11 / 1)', '8', '9'], 'current_status': 'Unsolvable', 'unsolvable_child': ['((11 / 1) + 8)', '9'], 'numbers': [1, 8, 9, 11]} |
graphcoloring_statetransition | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given a sequence of partial coloring states leading to the current coloring state S(i). The coloring state is a list, where each index represents th... | null | {'parent_state': [1, 1, 2, 3, 2, 3, 1, 1, 2, 3, 4, 5, 0, 0, 0, 0, 0, 0], 'current_state': [1, 1, 2, 3, 2, 3, 1, 1, 2, 3, 4, 5, 6, 0, 0, 0, 0, 0], 'current_status': 'Unsolvable', 'unsolvable_child': [1, 1, 2, 3, 2, 3, 1, 1, 2, 3, 4, 5, 6, 4, 0, 0, 0, 0], 'graph': [[3, 4, 5, 8, 10, 17], [2, 4, 11, 13, 14, 16], [1, 3, 5, ... |
game24_lookahead | You are given four numbers and the current calculation state for the Game of 24.
Your task is to determine if this current state can lead to a solvable solution. Specifically, use lookahead techniques to determine if the remaining numbers can be combined using basic arithmetic operations (+ - * /) to reach exactly 24. ... | (A) | null |
game24_statetransition | You are given an initial Game of 24 configuration S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid solu... | null | {'parent_state': ['4', '4', '11', '13'], 'current_state': ['(4 + 11)', '4', '13'], 'current_status': 'Solvable', 'unsolvable_child': ['((4 + 11) + 4)', '13'], 'numbers': [4, 4, 11, 13]} |
graphcoloring_lookahead | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given the current coloring state of the graph in a list, where each index represents the corresonding vertex, and the number at that index represent... | (A) | null |
graphcoloring_statetransition | You are given a graph represented as an adjacency list, where each index corresponds to a vertex, and the list at that index represents its adjacent vertices. You are also given a sequence of partial coloring states leading to the current coloring state S(i). The coloring state is a list, where each index represents th... | null | {'parent_state': [1, 2, 3, 2, 4, 5, 1, 6, 5, 7, 8, 0, 0, 0, 0, 0, 0, 0], 'current_state': [1, 2, 3, 2, 4, 5, 1, 6, 5, 7, 8, 4, 0, 0, 0, 0, 0, 0], 'current_status': 'Solvable', 'unsolvable_child': [1, 2, 3, 2, 4, 5, 1, 6, 5, 7, 8, 4, 9, 0, 0, 0, 0, 0], 'graph': [[1, 2, 3, 4, 5, 7, 9, 10, 11, 12, 15, 17], [0, 2, 7, 8, 9,... |
sudoku_statetransition | You are given an initial Sudoku puzzle S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid Sudoku solution... | null | {'parent_state': [[6, 7, 5, 2, 3, 9, 1, 4, 8], [1, 9, 4, 8, 7, 6, 3, 2, 5], [2, 8, 3, 1, 5, 4, 7, 9, 6], [5, 4, 1, 9, 6, 2, 8, 7, 3], [7, 6, 8, 4, 1, 3, 2, 5, 9], [3, 2, 9, 5, 8, 7, 4, 6, 1], [9, 3, 6, 7, 4, 8, 5, 1, 0], [0, 1, 2, 0, 9, 0, 0, 0, 7], [0, 5, 7, 6, 2, 0, 9, 3, 0]], 'current_state': [[6, 7, 5, 2, 3, 9, 1, ... |
sudoku_statetransition | You are given an initial Sudoku puzzle S(0), followed by a sequence of progressive states leading to the current state S(i). Alongside each state, its solvability status L(*) is given. Your task is to determine the next state by making exactly one move, ensuring progress toward a valid solution. A valid Sudoku solution... | null | {'parent_state': [[1, 6, 7, 2, 3, 8, 9, 4, 5], [2, 9, 3, 5, 4, 6, 8, 7, 1], [5, 4, 8, 1, 7, 9, 2, 6, 3], [3, 8, 1, 4, 6, 2, 5, 9, 7], [4, 0, 0, 7, 0, 1, 0, 8, 0], [0, 5, 0, 9, 0, 0, 0, 0, 4], [0, 0, 4, 0, 0, 0, 0, 3, 2], [0, 0, 2, 6, 1, 0, 4, 5, 0], [9, 7, 0, 0, 0, 0, 0, 0, 8]], 'current_state': [[1, 6, 7, 2, 3, 8, 9, ... |
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