跳马的乐趣和利润
Peg Jumping for Fun and Profit
摘要：
我们考虑的问题，确定所需的最小移动次数来解决一定的一维钉难题。设N为正整数。该拼图装置由一个具有单排2N+1个等间距孔的块组成，除了中心孔之外，这些孔被相等数量的N个红色和蓝色钉占据。该拼图的目的是通过一系列允许的移动来交换钉子的颜色。允许的移动有两种类型：一个桩可以从它所占据的洞移动到与它相邻的空洞，或者一个桩可以跳过相邻的桩进入空洞。我们展示了一个N^2+2N步的序列来解决这个难题，并证明了没有解决方案可以使用更少的移动。
英文摘要：
We consider the problem of determining the minimum number of moves needed to solve a certain one-dimensional peg puzzle. Let N be a positive integer. The puzzle apparatus consists of a block with a single row of 2N+1 equally spaced holes which, apart from the central hole, are occupied by an equal number N of red and blue pegs. The object of the puzzle is to exchange the colors of the pegs by a succession of allowable moves. Allowable moves are of two types: a peg can be shifted from the hole it occupies into the empty hole adjacent to it, or a peg can jump over an adjacent peg into the empty hole. We exhibit a sequence of N^2+2N moves that solves the puzzle, and prove that no solution can employ fewer moves.
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。
