Question

五个5，加减乘除四个符号 结果要等于4,四个符号不能重复

Answer 1

4种运算各用1次，所以任何2个5之间都必须填上1个运算符，不会出现55，555的情况。

按照实际计算的顺序，【相当于计算机计算时的顺序，也就是去掉括号后的计算顺序】，4个运算符只有4！= 4*3*2*1 = 24种。
因此，
5个5加减乘除各用1次，至多只有24个不同的结果。

下面列出这24种情形，
5+5 = 10, 10 - 5 = 5, 5*5 = 25, 25/5 = 5 [+-*/]
5+5 = 10, 10 - 5 = 5, 5/5 = 1, 1*5 = 5 [+-/*]
5+5 = 10, 10*5 = 50, 50-5 = 45, 45/5 = 9 [+*-/]
5+5 = 10, 10*5 = 50, 50/5 = 10, 10-5 = 5 [+*/-]
5+5 = 10, 10/5 = 2, 2-5 = -8, -8*5 = -40 [+/-*]
5+5 = 10, 10/5 = 2, 2*5 = 10, 10 - 5 = 5 [+/*-]

5 - 5 = 0, 0 + 5 = 5, 5*5 = 25, 25/5 = 5 [-+*/]
5 - 5 = 0, 0 + 5 = 5, 5/5 = 1, 1*5 = 5 [-+/*]
5 - 5 = 0, 0*5 = 0, 0 + 5 = 5, 5/5 = 1 [-*+/]
5 - 5 = 0, 0*5 = 0, 0/5 = 0, 0 + 5 = 5 [-*/+]
5 - 5 = 0, 0/5 = 0, 0 + 5 = 5, 5*5 = 25 [-/+*]
5 - 5 = 0, 0/5 = 0, 0*5 = 0, 0 + 5 = 5 [-/*+]

5*5 = 25, 25+5 = 30, 30-5 = 25, 25/5 = 5 [*+-/]
5*5 = 25, 25+5 = 30, 30/5 = 6, 6 - 5 = 1 [*+/-]
5*5 = 25, 25-5 = 20, 20+5 = 25, 25/5 = 5 [*-+/]
5*5 = 25, 25-5 = 20, 20/5 = 4, 4 + 5 = 9 [*-/+]
5*5 = 25, 25/5 = 5, 5 + 5 = 10, 10-5 = 5 [*/+-]
5*5 = 25, 25/5 = 5, 5-5 = 0, 0 + 5 = 5 [*/-+]

5/5 = 1, 1+5 = 6, 6 - 5 = 1, 1*5 = 5 [/+-*]
5/5 = 1, 1+5 = 6, 6*5 = 30, 30 - 5 = 25 [/+*-]
5/5 = 1, 1-5 = -4, -4+5 = 1, 1*5 = 5 [/-+*]
5/5 = 1, 1-5 = -4, -4*5 =-20,-20+5 = -15 [/-*+]
5/5 = 1, 1*5 = 5, 5 + 5 = 10, 10 - 5 = 5 [/*+-]
5/5 = 1, 1*5 = 5, 5 - 5 = 0, 0 + 5 = 5 [/*-+]

因为上面24个结果中没有4，
所以，
5个5加减乘除各用一次怎么也不可能等于4。

Answer 2

5-（5+5-5）/5=4