query: What is the average number of moves it takes to solve every 3x3 rubik’s cube position if only random moves are made?
positive_passages.docid: 17097
positive_passages.text: Number of moves necessary to solve Rubik's cube by pure chance
negative_passages.docid: 36805
negative_passages.text: Simple chessboard exercise
negative_passages.docid: 68793
negative_passages.text: Worst-case number of transpositions needed to generate a permutation
negative_passages.docid: 34452
negative_passages.text: In how many ways can you choose $k$ numbers out of $\{1,2,3,\dots,n\}$ so none of them is consecutive?
negative_passages.docid: 46999
negative_passages.text: How many fixed points in a permutation
negative_passages.docid: 68882
negative_passages.text: Path to Combinatorics Problem [$1.11$]
negative_passages.docid: 114228
negative_passages.text: Find the number of solutions to $ \lfloor x \rfloor + \lfloor 2x \rfloor + \lfloor 4x \rfloor + \ldots + \lfloor 32x \rfloor =12345$
negative_passages.docid: 125401
negative_passages.text: Mathematical Induction: Sum of first n odd perfect cubes
negative_passages.docid: 86233
negative_passages.text: A $3 \times 3 \times 3$ cube has no Hamiltonian path starting at the corner.
negative_passages.docid: 60661
negative_passages.text: How to solve this combination problem quickly?
negative_passages.docid: 15761
negative_passages.text: Rubik's Cube Combination
negative_passages.docid: 76370
negative_passages.text: Can any integer can be written as the sum of 8 integer cubes?
negative_passages.docid: 115852
negative_passages.text: Chess Piece Combinations
negative_passages.docid: 114752
negative_passages.text: Number of permutations of a specific cycle decomposition
negative_passages.docid: 10724
negative_passages.text: Case of the 'mice problem' for $n=3$
negative_passages.docid: 13822
negative_passages.text: Expected number of hamiltonian paths in a tournament
negative_passages.docid: 40508
negative_passages.text: How to generate Sudoku boards with unique solutions