论文标题
解决数字旋转难题的解决方案
Solution to the Number Rotation Puzzle
论文作者
论文摘要
数字旋转拼图（NRP）是一个组合拼图，在该难题中，目标是通过旋转的正方形块组成固定尺寸的旋转平方块，重新排列了拼命的矩形矩形网格。在所有可能的板和旋转块大小上，我们找到所有可解决的初始配置，并提供算法来求解此类配置。对于足够大的木板和旋转块大小，可溶解性条件仅取决于奇偶校验限制，并具有针对较小尺寸的特殊额外条件。一种特殊情况导致了$ s_6 $的异国外部自动形态的新颖构造。
The Number Rotation Puzzle (NRP) is a combination puzzle in which the goal is to rearrange a scrambled rectangular grid of numbers back into order via moves that consist of rotating square blocks of numbers of fixed size. Over all possible boards and rotating block sizes, we find all solvable initial configurations and provide algorithms to solve such configurations. For sufficiently large board and rotating block sizes, solvability conditions depend only on parity restrictions, with special additional conditions for smaller sizes. One special case leads to a novel construction of the exotic outer automorphism on $S_6$.
