珍珠湾ART

标题: 棋盘上的马 [打印本页]

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作者: fzy    时间: 2005-9-2 19:44
标题: 棋盘上的马

难度：++

1。证明在3X10的棋盘上，象棋中的马可以从任何一点出发，在30步内走遍所有30个点，最后回到出发点。

2。证明在4X10的棋盘上，上述走法不存在。

www.ddhw.com

 

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作者: sean9991    时间: 2005-9-2 21:07
标题: Famous knight's tour problem

There are six different solutions on a 3x10 table. www.ddhw.com

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作者: 野 菜 花    时间: 2005-9-4 22:50
标题: 第一题

3X10 的一 个走法 (是自己做的) www.ddhw.com 2www.ddhw.com 5www.ddhw.com 8 17www.ddhw.com 14www.ddhw.com 29 12www.ddhw.com 19www.ddhw.com 22 25www.ddhw.com 7www.ddhw.com 16 3www.ddhw.com 30www.ddhw.com 9www.ddhw.com 18 27www.ddhw.com 24www.ddhw.com 11www.ddhw.com 20 4www.ddhw.com 1www.ddhw.com 6www.ddhw.com 15 28www.ddhw.com 13www.ddhw.com 10www.ddhw.com 21 26www.ddhw.com 23  因为 1 和 30 首尾相接，所以从任何一个位置开始按这个顺序都可以走30步回到开始的位置。 www.ddhw.com

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作者: 寒潭清    时间: 2005-9-5 16:06
标题: [@};-][@};-][@};-][@};-]

  

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作者: fzy    时间: 2005-9-5 20:06
标题: Nicely done

Nicely Done! And how did you format it so well?www.ddhw.com   The solution is kind of unique. All variations (I believe there are 8) are more or less mirror images of each other. www.ddhw.com

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作者: 野 菜 花    时间: 2005-9-5 23:09
标题: 回复：Nicely done

Wow,  using simple mirror images of some parts, I got another three solutions easily! The original one: www.ddhw.com 2www.ddhw.com 5www.ddhw.com 8www.ddhw.com 17www.ddhw.com 14www.ddhw.com 29www.ddhw.com 12www.ddhw.com 19www.ddhw.com 22www.ddhw.com 25www.ddhw.com 7www.ddhw.com 16www.ddhw.com 3www.ddhw.com 30www.ddhw.com 9www.ddhw.com 18www.ddhw.com 27www.ddhw.com 24www.ddhw.com 11www.ddhw.com 20www.ddhw.com 4www.ddhw.com 1www.ddhw.com 6www.ddhw.com 15www.ddhw.com 28www.ddhw.com 13www.ddhw.com 10www.ddhw.com 21www.ddhw.com 26www.ddhw.com 23www.ddhw.com  Switch the two yellow rowswww.ddhw.com 4www.ddhw.com 1www.ddhw.com 6www.ddhw.com 17www.ddhw.com 14www.ddhw.com 29www.ddhw.com 12www.ddhw.com 19www.ddhw.com 22www.ddhw.com 25www.ddhw.com 7www.ddhw.com 16www.ddhw.com 3www.ddhw.com 30www.ddhw.com 9www.ddhw.com 18www.ddhw.com 27www.ddhw.com 24www.ddhw.com 11www.ddhw.com 20www.ddhw.com 2www.ddhw.com 5www.ddhw.com 8www.ddhw.com 15www.ddhw.com 28www.ddhw.com 13www.ddhw.com 10www.ddhw.com 21www.ddhw.com 26www.ddhw.com 23  Switch the two blue rows:www.ddhw.com 2www.ddhw.com 5www.ddhw.com 8www.ddhw.com 15www.ddhw.com 28www.ddhw.com 13www.ddhw.com 10www.ddhw.com 19www.ddhw.com 22www.ddhw.com 25www.ddhw.com 7www.ddhw.com 16www.ddhw.com 3www.ddhw.com 30www.ddhw.com 9www.ddhw.com 18www.ddhw.com 27www.ddhw.com 24www.ddhw.com 11www.ddhw.com 20www.ddhw.com 4www.ddhw.com 1www.ddhw.com 6www.ddhw.com 17www.ddhw.com 14www.ddhw.com 29www.ddhw.com 12 21www.ddhw.com 26www.ddhw.com 23  Switch the two red rows:www.ddhw.com 2www.ddhw.com 5www.ddhw.com 8www.ddhw.com 17www.ddhw.com 14www.ddhw.com 29www.ddhw.com 12www.ddhw.com 21www.ddhw.com 26www.ddhw.com 23www.ddhw.com 7www.ddhw.com 16www.ddhw.com 3www.ddhw.com 30www.ddhw.com 9www.ddhw.com 18www.ddhw.com 27www.ddhw.com 24www.ddhw.com 11www.ddhw.com 20www.ddhw.com 4www.ddhw.com 1www.ddhw.com 6www.ddhw.com 作者: fzy    时间: 2005-9-6 00:50 标题: 回复：回复：Nicely done And by taking full mirror images of the 4, we get 4 more, and I believe they are all the possible solutions. www.ddhw.com   Yes, that is what I mean by format. Looks really nice. www.ddhw.com   欢迎光临 珍珠湾ART (http://69.48.205.96:9997/) Powered by Discuz! X3