组合问题：将 1,2,3,4 填进正方形四个顶点，使相邻顶点数字之和为质数，有几种填法？

popo987654

请问有什么方法可以不重不漏的算出来，想学习，我算来算去都错...

Treenewbee

1. sol=Select[Tuples[Range@4,{4}],AllTrue[Total/@Partition[#,2,1,1],PrimeQ]&]

复制代码

{{1,1,1,1},{1,1,1,2},{1,1,1,4},{1,1,2,1},{1,1,4,1},{1,2,1,1},{1,2,1,2},{1,2,1,4},{1,2,3,2},{1,2,3,4},{1,4,1,1},{1,4,1,2},{1,4,1,4},{1,4,3,2},{1,4,3,4},{2,1,1,1},{2,1,2,1},{2,1,2,3},{2,1,4,1},{2,1,4,3},{2,3,2,1},{2,3,2,3},{2,3,4,1},{2,3,4,3},{3,2,1,2},{3,2,1,4},{3,2,3,2},{3,2,3,4},{3,4,1,2},{3,4,1,4},{3,4,3,2},{3,4,3,4},{4,1,1,1},{4,1,2,1},{4,1,2,3},{4,1,4,1},{4,1,4,3},{4,3,2,1},{4,3,2,3},{4,3,4,1},{4,3,4,3}}

共41种方法