魔方吧·中文魔方俱乐部

标题: 一个“碰手游戏”，是不是有必胜法 [打印本页]

作者: jimofc 时间: 2012-4-8 23:39:20 标题: 一个“碰手游戏”，是不是有必胜法

今天下午某妹子和我玩了个游戏，

游戏规则：
1，两个人都伸出手，用手表示数字0-9，每个人的开始时都是两个”1“
现在用【1,1】【1,1】代表两个人左右手的数字

2，然后从第一个人开始，用自己某个手去碰对方的手，然后自己碰的手上的数字变成这两只手数字之和，交替进行，自己的手不能与自己的手碰。
比如【1,2】【3,4】，第一个人行动，用1碰4，变成【5,2】【3,4】，然后轮到另一人行动

3，如果数字大于10，那么就减去10为结果
比如【5,6】【7,8】，第一个人行动，用5碰7，变成【2，6】【7,8】

4，如果碰完某只手的数字为10，那么这只手退出游戏
比如【5,6】【4,8】，第一个人行动，用6碰4，变成【5】【4,8】

5，当一方的两只手全退出游戏了，获得胜利。

问：这个游戏先手可不可以必胜？
另外，通过游戏发现，两个人只剩下一只手时可能没有循环状态导致平局出现【有待验证】

下午玩的时候就在考虑一些战术，比如手里始终控制一个5或者9之类的，
必胜法应该是有的，因为每次可以选择的碰撞方式最多有4种，起始时也是固定开局，那么双方一定有一个共同的”最优玩法“
如果步数不太多的话可以考虑穷举，现在正尝试编程求解。

然后，对这个游戏进行改进，开局时可以自己任选俩个不为0的数字，那么有什么技巧，或者运气的成分比较大？
如果是多人进行会怎样？

作者: Cielo 时间: 2012-4-8 23:56:05

这个，亮点是第一句吧

作者: 小熊猫 时间: 2012-4-9 00:18:18

原来玩过必胜方法。。坐等高人！

作者: jimofc 时间: 2012-4-9 07:33:56

原帖由 Cielo 于 2012-4-8 23:56 发表
这个，亮点是第一句吧

呃。。。还是问题比较重要一些。。。

作者: ursace 时间: 2012-4-9 10:29:08

本帖的亮点在“妹子”，其他的都没看见

作者: jimofc 时间: 2012-4-9 10:34:57 标题: 标题

原帖由 ursace 于 2012-4-9 10:29 发表
本帖的亮点在“妹子”，其他的都没看见

要思考问题啊-_-!不要因为两个字忽略了我打的那么多字。。。

作者: jimofc 时间: 2012-4-9 10:38:40

刚才试着写了几段程序，类似象棋，猜想如果两个人都使用最优解法，可能出现平局

作者: phileas 时间: 2012-4-9 14:11:06

双方各剩一只手时，可能出现和局，其中一个解是【1】【8】

作者: lulijie 时间: 2012-4-9 21:20:26

以前有魔友发过该贴，当时他没有说清楚游戏规则
http://bbs.mf8-china.com/viewthr ... CE%CF%B7&page=1

作者: lulijie 时间: 2012-4-10 20:53:22

先行方的两个数字为a1,b1，对方的两个数字为a2,b2
用f(a2,b2,a1,b1)的值表示结果。
f(a2,b2,a1,b1)＝1，表示先行方必败。
f(a2,b2,a1,b1)＝2，表示先行方必胜。
f(a2,b2,a1,b1)＝3，表示和局。
f(a2,b2,a1,b1)＝0，表示结果待定。
编程计算得

作者: lulijie 时间: 2012-4-10 20:54:31

f(0,1,0,5)=1
f(0,1,0,6)=1
f(0,1,0,8)=1
f(0,1,1,9)=1
f(0,1,4,4)=1
f(0,1,6,9)=1
f(0,1,7,9)=1
f(0,1,8,8)=1
f(0,1,9,9)=1
f(0,2,0,1)=1
f(0,2,0,3)=1
f(0,2,0,6)=1
f(0,2,1,7)=1
f(0,2,2,2)=1
f(0,2,2,6)=1
f(0,2,2,8)=1
f(0,2,3,8)=1
f(0,2,4,4)=1
f(0,2,4,6)=1
f(0,2,5,8)=1
f(0,2,6,6)=1
f(0,2,6,7)=1
f(0,2,7,7)=1
f(0,2,7,9)=1
f(0,2,8,8)=1
f(0,2,9,9)=1
f(0,3,0,4)=1
f(0,3,0,5)=1
f(0,3,0,8)=1
f(0,3,1,7)=1
f(0,3,2,2)=1
f(0,3,3,7)=1
f(0,3,4,4)=1
f(0,3,7,7)=1
f(0,3,7,8)=1
f(0,4,0,1)=1
f(0,4,0,2)=1
f(0,4,0,7)=1
f(0,4,1,6)=1
f(0,4,2,2)=1
f(0,4,2,4)=1
f(0,4,2,8)=1
f(0,4,2,9)=1
f(0,4,3,3)=1
f(0,4,3,9)=1
f(0,4,4,4)=1
f(0,4,4,6)=1
f(0,4,5,6)=1
f(0,4,6,6)=1
f(0,4,7,9)=1
f(0,4,8,8)=1
f(0,4,9,9)=1
f(0,5,0,1)=1
f(0,5,0,3)=1
f(0,5,0,7)=1
f(0,5,0,9)=1
f(0,5,1,9)=1
f(0,5,2,5)=1
f(0,5,2,8)=1
f(0,5,3,7)=1
f(0,5,4,5)=1
f(0,5,4,6)=1
f(0,5,5,5)=1
f(0,5,5,6)=1
f(0,5,5,8)=1
f(0,6,0,3)=1
f(0,6,0,8)=1
f(0,6,0,9)=1
f(0,6,1,1)=1
f(0,6,1,3)=1
f(0,6,1,7)=1
f(0,6,1,8)=1
f(0,6,2,2)=1
f(0,6,2,8)=1
f(0,6,4,4)=1
f(0,6,4,5)=1
f(0,6,4,6)=1
f(0,6,4,9)=1
f(0,6,6,6)=1
f(0,6,6,8)=1
f(0,6,7,7)=1
f(0,6,8,8)=1
f(0,7,0,2)=1
f(0,7,0,5)=1
f(0,7,0,6)=1
f(0,7,2,3)=1
f(0,7,3,3)=1
f(0,7,3,7)=1
f(0,7,3,9)=1
f(0,7,6,6)=1
f(0,7,8,8)=1
f(0,8,0,4)=1
f(0,8,0,7)=1
f(0,8,0,9)=1
f(0,8,1,1)=1
f(0,8,1,3)=1
f(0,8,2,2)=1
f(0,8,2,5)=1
f(0,8,2,7)=1
f(0,8,2,8)=1
f(0,8,3,3)=1
f(0,8,3,4)=1
f(0,8,3,9)=1
f(0,8,4,4)=1
f(0,8,4,6)=1
f(0,8,4,8)=1
f(0,8,6,6)=1
f(0,8,8,8)=1
f(0,9,0,2)=1
f(0,9,0,4)=1
f(0,9,0,5)=1
f(0,9,1,1)=1
f(0,9,1,3)=1
f(0,9,1,4)=1
f(0,9,1,9)=1
f(0,9,2,2)=1
f(0,9,6,6)=1
f(1,1,0,3)=1
f(1,5,0,4)=1
f(3,3,0,9)=1
f(3,5,0,2)=1
f(5,7,0,8)=1
f(5,9,0,6)=1
f(7,7,0,1)=1
f(9,9,0,7)=1

作者: lulijie 时间: 2012-4-10 20:56:29

f(0,1,0,1)=2
f(0,1,0,3)=2
f(0,1,0,4)=2
f(0,1,0,9)=2
f(0,1,2,9)=2
f(0,1,4,9)=2
f(0,1,5,9)=2
f(0,1,6,7)=2
f(0,2,0,2)=2
f(0,2,0,5)=2
f(0,2,0,7)=2
f(0,2,0,8)=2
f(0,2,1,5)=2
f(0,2,3,3)=2
f(0,2,4,8)=2
f(0,2,7,8)=2
f(0,2,8,9)=2
f(0,3,0,2)=2
f(0,3,0,3)=2
f(0,3,0,7)=2
f(0,3,0,9)=2
f(0,3,1,8)=2
f(0,3,2,7)=2
f(0,3,5,7)=2
f(0,3,6,7)=2
f(0,4,0,4)=2
f(0,4,0,5)=2
f(0,4,0,6)=2
f(0,4,0,9)=2
f(0,4,1,1)=2
f(0,4,3,6)=2
f(0,4,5,7)=2
f(0,4,6,8)=2
f(0,4,6,9)=2
f(0,5,0,2)=2
f(0,5,0,4)=2
f(0,5,0,5)=2
f(0,5,0,6)=2
f(0,5,0,8)=2
f(0,5,1,5)=2
f(0,5,3,5)=2
f(0,5,5,7)=2
f(0,5,5,9)=2
f(0,6,0,1)=2
f(0,6,0,4)=2
f(0,6,0,5)=2
f(0,6,0,6)=2
f(0,6,1,4)=2
f(0,6,2,4)=2
f(0,6,3,5)=2
f(0,6,4,7)=2
f(0,6,9,9)=2
f(0,7,0,1)=2
f(0,7,0,3)=2
f(0,7,0,7)=2
f(0,7,0,8)=2
f(0,7,2,9)=2
f(0,7,3,4)=2
f(0,7,3,5)=2
f(0,7,3,8)=2
f(0,8,0,2)=2
f(0,8,0,3)=2
f(0,8,0,5)=2
f(0,8,0,8)=2
f(0,8,1,2)=2
f(0,8,2,3)=2
f(0,8,2,6)=2
f(0,8,5,9)=2
f(0,8,7,7)=2
f(0,9,0,1)=2
f(0,9,0,6)=2
f(0,9,0,7)=2
f(0,9,0,9)=2
f(0,9,1,5)=2
f(0,9,1,6)=2
f(0,9,1,8)=2
f(0,9,3,4)=2
f(1,1,0,5)=2
f(1,1,0,7)=2
f(1,1,0,8)=2
f(1,1,0,9)=2
f(1,1,6,9)=2
f(1,1,8,9)=2
f(1,1,9,9)=2
f(1,2,0,8)=2
f(1,2,0,9)=2
f(1,3,0,3)=2
f(1,3,0,5)=2
f(1,3,0,6)=2
f(1,3,0,7)=2
f(1,3,0,8)=2
f(1,3,0,9)=2
f(1,3,6,7)=2
f(1,3,6,9)=2
f(1,3,7,8)=2
f(1,3,7,9)=2
f(1,3,8,9)=2
f(1,3,9,9)=2
f(1,4,0,5)=2
f(1,4,0,6)=2
f(1,4,0,8)=2
f(1,4,0,9)=2
f(1,4,6,9)=2
f(1,4,9,9)=2
f(1,5,0,5)=2
f(1,5,0,9)=2
f(1,6,0,3)=2
f(1,6,0,4)=2
f(1,6,0,8)=2
f(1,6,0,9)=2
f(1,6,4,4)=2
f(1,6,4,9)=2
f(1,7,0,1)=2
f(1,7,0,2)=2
f(1,7,0,3)=2
f(1,7,0,5)=2
f(1,7,0,6)=2
f(1,7,0,9)=2
f(1,7,2,3)=2
f(1,7,2,9)=2
f(1,7,3,3)=2
f(1,7,3,6)=2
f(1,7,3,9)=2
f(1,7,6,9)=2
f(1,8,0,2)=2
f(1,8,0,5)=2
f(1,8,0,8)=2
f(1,8,0,9)=2
f(1,8,2,6)=2
f(1,8,6,9)=2
f(1,9,0,1)=2
f(1,9,0,2)=2
f(1,9,0,4)=2
f(1,9,0,6)=2
f(1,9,0,8)=2
f(1,9,0,9)=2
f(1,9,1,1)=2
f(1,9,1,5)=2
f(1,9,1,9)=2
f(1,9,5,9)=2
f(1,9,9,9)=2
f(2,2,0,1)=2
f(2,2,0,2)=2
f(2,2,0,4)=2
f(2,2,0,6)=2
f(2,2,0,7)=2
f(2,2,0,8)=2
f(2,2,2,8)=2
f(2,2,3,8)=2
f(2,2,4,8)=2
f(2,2,6,8)=2
f(2,2,8,8)=2
f(2,2,8,9)=2
f(2,3,0,4)=2
f(2,3,0,5)=2
f(2,3,0,7)=2
f(2,3,0,8)=2
f(2,3,7,7)=2
f(2,3,7,8)=2
f(2,4,0,2)=2
f(2,4,0,6)=2
f(2,4,0,8)=2
f(2,4,4,6)=2
f(2,4,4,8)=2
f(2,5,0,3)=2
f(2,5,0,5)=2
f(2,5,0,6)=2
f(2,5,0,8)=2
f(2,5,5,5)=2
f(2,5,5,8)=2
f(2,5,8,8)=2
f(2,6,0,4)=2
f(2,6,0,6)=2
f(2,6,0,8)=2
f(2,6,2,4)=2
f(2,6,2,8)=2
f(2,7,0,1)=2
f(2,7,0,3)=2
f(2,7,0,6)=2
f(2,7,0,8)=2
f(2,7,3,8)=2
f(2,7,8,8)=2
f(2,8,0,2)=2
f(2,8,0,3)=2
f(2,8,0,4)=2
f(2,8,0,6)=2
f(2,8,0,7)=2
f(2,8,0,8)=2
f(2,8,2,2)=2
f(2,8,2,4)=2
f(2,8,2,5)=2
f(2,8,2,6)=2
f(2,8,2,8)=2
f(2,8,4,8)=2
f(2,8,5,8)=2
f(2,8,6,8)=2
f(2,8,8,8)=2
f(2,9,0,1)=2
f(2,9,0,2)=2
f(2,9,0,5)=2
f(2,9,0,8)=2
f(2,9,1,4)=2
f(2,9,4,8)=2
f(3,3,0,1)=2
f(3,3,0,4)=2
f(3,3,0,5)=2
f(3,3,0,7)=2
f(3,3,4,7)=2
f(3,3,7,7)=2
f(3,3,7,8)=2
f(3,4,0,4)=2
f(3,4,0,5)=2
f(3,4,0,6)=2
f(3,4,0,7)=2
f(3,4,6,8)=2
f(3,4,7,8)=2
f(3,5,0,5)=2
f(3,5,0,7)=2
f(3,6,0,4)=2
f(3,6,0,7)=2
f(3,7,0,2)=2
f(3,7,0,3)=2
f(3,7,0,4)=2
f(3,7,0,6)=2
f(3,7,0,7)=2
f(3,7,0,8)=2
f(3,7,3,3)=2
f(3,7,3,5)=2
f(3,7,3,7)=2
f(3,7,5,7)=2
f(3,7,7,7)=2
f(3,8,0,2)=2
f(3,8,0,4)=2
f(3,8,0,7)=2
f(3,8,0,9)=2
f(3,8,2,2)=2
f(3,8,2,7)=2
f(3,9,0,1)=2
f(3,9,0,4)=2
f(3,9,0,5)=2
f(3,9,0,7)=2
f(3,9,0,8)=2
f(3,9,0,9)=2
f(3,9,1,4)=2
f(3,9,1,7)=2
f(3,9,1,8)=2
f(3,9,4,7)=2
f(3,9,7,7)=2
f(3,9,7,8)=2
f(4,4,0,2)=2
f(4,4,0,4)=2
f(4,4,0,6)=2
f(4,4,0,7)=2
f(4,4,0,8)=2
f(4,4,0,9)=2
f(4,4,1,6)=2
f(4,4,2,6)=2
f(4,4,3,6)=2
f(4,4,4,6)=2
f(4,4,6,6)=2
f(4,4,6,8)=2
f(4,5,0,1)=2
f(4,5,0,2)=2
f(4,5,0,5)=2
f(4,5,0,6)=2
f(4,5,5,5)=2
f(4,5,5,6)=2
f(4,5,6,6)=2
f(4,6,0,1)=2
f(4,6,0,2)=2
f(4,6,0,4)=2
f(4,6,0,6)=2
f(4,6,0,8)=2
f(4,6,0,9)=2
f(4,6,2,4)=2
f(4,6,2,6)=2
f(4,6,4,4)=2
f(4,6,4,5)=2
f(4,6,4,6)=2
f(4,6,4,8)=2
f(4,6,5,6)=2
f(4,6,6,6)=2
f(4,6,6,8)=2
f(4,7,0,3)=2
f(4,7,0,6)=2
f(4,8,0,2)=2
f(4,8,0,4)=2
f(4,8,0,6)=2
f(4,8,2,8)=2
f(4,8,6,8)=2
f(4,9,0,1)=2
f(4,9,0,2)=2
f(4,9,0,6)=2
f(4,9,0,7)=2
f(4,9,1,6)=2
f(4,9,6,6)=2
f(5,5,0,5)=2
f(5,5,5,5)=2
f(5,6,0,4)=2
f(5,6,0,5)=2
f(5,6,0,8)=2
f(5,6,0,9)=2
f(5,6,4,4)=2
f(5,6,4,5)=2
f(5,6,5,5)=2
f(5,7,0,3)=2
f(5,7,0,5)=2
f(5,8,0,2)=2
f(5,8,0,4)=2
f(5,8,0,5)=2
f(5,8,0,7)=2
f(5,8,2,2)=2
f(5,8,2,5)=2
f(5,8,5,5)=2
f(5,9,0,1)=2
f(5,9,0,5)=2
f(6,6,0,1)=2
f(6,6,0,2)=2
f(6,6,0,3)=2
f(6,6,0,4)=2
f(6,6,0,6)=2
f(6,6,0,8)=2
f(6,6,2,4)=2
f(6,6,4,4)=2
f(6,6,4,6)=2
f(6,6,4,7)=2
f(6,6,4,8)=2
f(6,6,4,9)=2
f(6,7,0,3)=2
f(6,7,0,4)=2
f(6,7,0,5)=2
f(6,7,0,6)=2
f(6,7,2,3)=2
f(6,7,2,4)=2
f(6,8,0,2)=2
f(6,8,0,4)=2
f(6,8,0,8)=2
f(6,8,2,6)=2
f(6,8,4,6)=2
f(6,9,0,1)=2
f(6,9,0,2)=2
f(6,9,0,4)=2
f(6,9,0,5)=2
f(6,9,1,1)=2
f(6,9,1,4)=2
f(7,7,0,3)=2
f(7,7,0,5)=2
f(7,7,0,6)=2
f(7,7,0,9)=2
f(7,7,2,3)=2
f(7,7,3,3)=2
f(7,7,3,6)=2
f(7,8,0,2)=2
f(7,8,0,3)=2
f(7,8,0,5)=2
f(7,8,0,6)=2
f(7,8,2,3)=2
f(7,8,3,3)=2
f(7,9,0,1)=2
f(7,9,0,2)=2
f(7,9,0,3)=2
f(7,9,0,4)=2
f(7,9,0,5)=2
f(7,9,0,7)=2
f(7,9,1,1)=2
f(7,9,1,2)=2
f(7,9,1,3)=2
f(7,9,1,4)=2
f(7,9,2,3)=2
f(7,9,3,4)=2
f(8,8,0,2)=2
f(8,8,0,3)=2
f(8,8,0,4)=2
f(8,8,0,6)=2
f(8,8,0,8)=2
f(8,8,0,9)=2
f(8,8,1,2)=2
f(8,8,2,2)=2
f(8,8,2,4)=2
f(8,8,2,6)=2
f(8,8,2,7)=2
f(8,8,2,8)=2
f(8,9,0,1)=2
f(8,9,0,2)=2
f(9,9,0,1)=2
f(9,9,0,2)=2
f(9,9,0,3)=2
f(9,9,0,5)=2
f(9,9,1,1)=2
f(9,9,1,2)=2
f(9,9,1,4)=2

作者: lulijie 时间: 2012-4-10 20:59:04

f(0,1,0,2)=3
f(0,1,0,7)=3
f(0,1,1,7)=3
f(0,1,2,6)=3
f(0,1,3,5)=3
f(0,1,3,9)=3
f(0,1,8,9)=3
f(0,2,0,4)=3
f(0,2,0,9)=3
f(0,2,1,8)=3
f(0,2,2,4)=3
f(0,2,6,8)=3
f(0,3,0,1)=3
f(0,3,0,6)=3
f(0,3,1,3)=3
f(0,3,4,7)=3
f(0,3,5,9)=3
f(0,3,6,8)=3
f(0,3,7,9)=3
f(0,4,0,3)=3
f(0,4,0,8)=3
f(0,4,2,6)=3
f(0,4,4,8)=3
f(0,4,6,7)=3
f(0,6,0,2)=3
f(0,6,0,7)=3
f(0,6,2,6)=3
f(0,6,3,4)=3
f(0,6,4,8)=3
f(0,7,0,4)=3
f(0,7,0,9)=3
f(0,7,1,3)=3
f(0,7,1,5)=3
f(0,7,2,4)=3
f(0,7,3,6)=3
f(0,7,7,9)=3
f(0,8,0,1)=3
f(0,8,0,6)=3
f(0,8,2,4)=3
f(0,8,2,9)=3
f(0,8,6,8)=3
f(0,9,0,3)=3
f(0,9,0,8)=3
f(0,9,1,2)=3
f(0,9,1,7)=3
f(0,9,3,9)=3
f(0,9,4,8)=3
f(0,9,5,7)=3
f(1,2,0,7)=3
f(1,8,0,1)=3
f(2,2,2,4)=3
f(2,2,6,6)=3
f(2,4,0,4)=3
f(2,4,2,6)=3
f(2,4,2,8)=3
f(2,4,4,4)=3
f(2,4,6,6)=3
f(2,4,6,8)=3
f(2,4,8,8)=3
f(2,6,0,2)=3
f(2,6,2,2)=3
f(2,6,4,4)=3
f(2,6,4,6)=3
f(2,6,4,8)=3
f(2,6,6,8)=3
f(2,6,8,8)=3
f(2,9,0,9)=3
f(3,4,0,3)=3
f(3,6,0,1)=3
f(4,4,2,2)=3
f(4,4,4,8)=3
f(4,7,0,9)=3
f(4,8,0,8)=3
f(4,8,2,2)=3
f(4,8,2,4)=3
f(4,8,2,6)=3
f(4,8,4,6)=3
f(4,8,6,6)=3
f(4,8,8,8)=3
f(6,6,2,6)=3
f(6,6,8,8)=3
f(6,7,0,7)=3
f(6,8,0,6)=3
f(6,8,2,2)=3
f(6,8,2,4)=3
f(6,8,2,8)=3
f(6,8,4,4)=3
f(6,8,4,8)=3
f(6,8,6,6)=3
f(8,8,4,4)=3
f(8,8,6,8)=3
f(8,9,0,3)=3

作者: lulijie 时间: 2012-4-10 21:01:38

其余的总共有2280个局面无法获取结果，即f()=0。包括f(1,1,1,1)

作者: jimofc 时间: 2012-4-11 08:13:31

原帖由 lulijie 于 2012-4-10 21:01 发表
其余的总共有2280个局面无法获取结果，即f()=0。包括f(1,1,1,1)

那么就是说1111的初始开局，两个人都可以通过合理选择而达到平局，当有人失误的时候才会输，这个游戏是公平的

作者: phileas 时间: 2012-4-11 13:41:34

为啥有四种情况？ 0和3有什么不同？

作者: lulijie 时间: 2012-4-11 20:35:16

3是和，
0表示待定，或1或2或3,不过还没确定。

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