如下图所示,在圆周上,放置互不相同的5个正整数,要求每相邻的3个正整数的和不超过21,则这5个正整数之和是要最大值

Question

如下图所示,在圆周上,放置互不相同的5个正整数,要求每相邻的3个正整数的和不超过21,则这5个正整数之和是
要最大值

Answer 1

X1,X2,X3,X4,X5
X1+X2+X3<=21 X2+X3+X4<=21 X3+X4+X5<=21 X4+X5+X1<=21 X5+X1+X2<=21
(X1+X2+X3)+( X2+X3+X4)+( X3+X4+X5)+(X4+X5+X1)+( X5+X1+X2)<=21+21+21+21+21
2X1+3X2+3X3+3X4+3X5<=105
3(X1+X2+X3+X4+X5)<=105+X1
1+2+18=21
X1=11 3(X1+X2+X3+X4+X5)<=105+X1=123 X1+X2+X3+X4+X5<=41
最大值41