Gourds：一个带旋转的滑块拼图
Gourds: a sliding-block puzzle with turning
摘要：
我们提出了一种新的滑块拼图，称为葫芦，其中的目标是重新安排1 × 2块上的六边形网格板的2n + 1细胞与n件，使用滑动，转动和旋转移动。这个谜题在棋盘上有一个空的单元格，形成了15-谜题的自然延伸，包括旋转移动。我们分析的难题，并完全表征的情况下，难题总是可以解决的。我们还研究了确定一组给定的彩色件是否可以放置在一个彩色的六边形网格板与匹配的颜色的复杂性。我们证明了这个问题对于任意多个颜色是NP完全的，但是如果颜色的数量是一个固定的常数，则在随机多项式时间内是可解的。
英文摘要：
We propose a new kind of sliding-block puzzle, called Gourds, where the objective is to rearrange 1 x 2 pieces on a hexagonal grid board of 2n + 1 cells with n pieces, using sliding, turning and pivoting moves. This puzzle has a single empty cell on a board and forms a natural extension of the 15-puzzle to include rotational moves. We analyze the puzzle and completely characterize the cases when the puzzle can always be solved. We also study the complexity of determining whether a given set of colored pieces can be placed on a colored hexagonal grid board with matching colors. We show this problem is NP-complete for arbitrarily many colors, but solvable in randomized polynomial time if the number of colors is a fixed constant.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
