Question

钟面上有1,2,3.....，11,12共12个数字，试在某些数字前加上负号，使他们的和等于零；你发现了什么规律？

Answer 1

（1）124组任选
1+2+3+4+5+6+7-8-9-10+11-12 = 0
1+2+3+4+5+6-7+8-9+10-11-12 = 0
1+2+3+4+5-6+7+8+9-10-11-12 = 0
1+2+3+4-5+6-7-8-9-10+11+12 = 0
1+2+3+4-5-6+7-8-9+10-11+12 = 0
1+2+3+4-5-6-7+8+9-10-11+12 = 0
1+2+3+4-5-6-7+8-9+10+11-12 = 0
1+2+3-4+5+6-7-8-9+10-11+12 = 0
1+2+3-4+5-6+7-8+9-10-11+12 = 0
1+2+3-4+5-6+7-8-9+10+11-12 = 0
1+2+3-4+5-6-7+8+9-10+11-12 = 0
1+2+3-4-5+6+7+8-9-10-11+12 = 0
1+2+3-4-5+6+7-8+9-10+11-12 = 0
1+2+3-4-5+6-7+8+9+10-11-12 = 0
1+2+3-4-5-6-7-8-9+10+11+12 = 0
1+2-3+4+5+6-7-8+9-10-11+12 = 0
1+2-3+4+5+6-7-8-9+10+11-12 = 0
1+2-3+4+5-6+7+8-9-10-11+12 = 0
1+2-3+4+5-6+7-8+9-10+11-12 = 0
1+2-3+4+5-6-7+8+9+10-11-12 = 0
1+2-3+4-5+6+7+8-9-10+11-12 = 0
1+2-3+4-5+6+7-8+9+10-11-12 = 0
1+2-3+4-5-6-7-8+9-10+11+12 = 0
1+2-3-4+5+6+7+8-9+10-11-12 = 0
1+2-3-4+5-6-7+8-9-10+11+12 = 0
1+2-3-4+5-6-7-8+9+10-11+12 = 0
1+2-3-4-5+6+7-8-9-10+11+12 = 0
1+2-3-4-5+6-7+8-9+10-11+12 = 0
1+2-3-4-5+6-7-8+9+10+11-12 = 0
1+2-3-4-5-6+7+8+9-10-11+12 = 0
1+2-3-4-5-6+7+8-9+10+11-12 = 0
1-2+3+4+5+6-7+8-9-10-11+12 = 0
1-2+3+4+5+6-7-8+9-10+11-12 = 0
1-2+3+4+5-6+7+8-9-10+11-12 = 0
1-2+3+4+5-6+7-8+9+10-11-12 = 0
1-2+3+4-5+6+7+8-9+10-11-12 = 0
1-2+3+4-5-6-7+8-9-10+11+12 = 0
1-2+3+4-5-6-7-8+9+10-11+12 = 0
1-2+3-4+5+6+7+8+9-10-11-12 = 0
1-2+3-4+5-6+7-8-9-10+11+12 = 0
1-2+3-4+5-6-7+8-9+10-11+12 = 0
1-2+3-4+5-6-7-8+9+10+11-12 = 0
1-2+3-4-5+6+7-8-9+10-11+12 = 0
1-2+3-4-5+6-7+8+9-10-11+12 = 0
1-2+3-4-5+6-7+8-9+10+11-12 = 0
1-2+3-4-5-6+7+8+9-10+11-12 = 0
1-2-3+4+5+6-7-8-9-10+11+12 = 0
1-2-3+4+5-6+7-8-9+10-11+12 = 0
1-2-3+4+5-6-7+8+9-10-11+12 = 0
1-2-3+4+5-6-7+8-9+10+11-12 = 0
1-2-3+4-5+6+7-8+9-10-11+12 = 0
1-2-3+4-5+6+7-8-9+10+11-12 = 0
1-2-3+4-5+6-7+8+9-10+11-12 = 0
1-2-3+4-5-6+7+8+9+10-11-12 = 0
1-2-3-4+5+6+7+8-9-10-11+12 = 0
1-2-3-4+5+6+7-8+9-10+11-12 = 0
1-2-3-4+5+6-7+8+9+10-11-12 = 0
1-2-3-4+5-6-7-8-9+10+11+12 = 0
1-2-3-4-5+6-7-8+9-10+11+12 = 0
1-2-3-4-5-6+7+8-9-10+11+12 = 0
1-2-3-4-5-6+7-8+9+10-11+12 = 0
1-2-3-4-5-6-7+8+9+10+11-12 = 0
-1+2+3+4+5+6+7-8-9-10-11+12 = 0
-1+2+3+4+5+6-7+8-9-10+11-12 = 0
-1+2+3+4+5+6-7-8+9+10-11-12 = 0
-1+2+3+4+5-6+7+8-9+10-11-12 = 0
-1+2+3+4-5+6+7+8+9-10-11-12 = 0
-1+2+3+4-5-6+7-8-9-10+11+12 = 0
-1+2+3+4-5-6-7+8-9+10-11+12 = 0
-1+2+3+4-5-6-7-8+9+10+11-12 = 0
-1+2+3-4+5+6-7-8-9-10+11+12 = 0
-1+2+3-4+5-6+7-8-9+10-11+12 = 0
-1+2+3-4+5-6-7+8+9-10-11+12 = 0
-1+2+3-4+5-6-7+8-9+10+11-12 = 0
-1+2+3-4-5+6+7-8+9-10-11+12 = 0
-1+2+3-4-5+6+7-8-9+10+11-12 = 0
-1+2+3-4-5+6-7+8+9-10+11-12 = 0
-1+2+3-4-5-6+7+8+9+10-11-12 = 0
-1+2-3+4+5+6-7-8-9+10-11+12 = 0
-1+2-3+4+5-6+7-8+9-10-11+12 = 0
-1+2-3+4+5-6+7-8-9+10+11-12 = 0
-1+2-3+4+5-6-7+8+9-10+11-12 = 0
-1+2-3+4-5+6+7+8-9-10-11+12 = 0
-1+2-3+4-5+6+7-8+9-10+11-12 = 0
-1+2-3+4-5+6-7+8+9+10-11-12 = 0
-1+2-3+4-5-6-7-8-9+10+11+12 = 0
-1+2-3-4+5+6+7+8-9-10+11-12 = 0
-1+2-3-4+5+6+7-8+9+10-11-12 = 0
-1+2-3-4+5-6-7-8+9-10+11+12 = 0
-1+2-3-4-5+6-7+8-9-10+11+12 = 0
-1+2-3-4-5+6-7-8+9+10-11+12 = 0
-1+2-3-4-5-6+7+8-9+10-11+12 = 0
-1+2-3-4-5-6+7-8+9+10+11-12 = 0
-1-2+3+4+5+6-7-8+9-10-11+12 = 0
-1-2+3+4+5+6-7-8-9+10+11-12 = 0
-1-2+3+4+5-6+7+8-9-10-11+12 = 0
-1-2+3+4+5-6+7-8+9-10+11-12 = 0
-1-2+3+4+5-6-7+8+9+10-11-12 = 0
-1-2+3+4-5+6+7+8-9-10+11-12 = 0
-1-2+3+4-5+6+7-8+9+10-11-12 = 0
-1-2+3+4-5-6-7-8+9-10+11+12 = 0
-1-2+3-4+5+6+7+8-9+10-11-12 = 0
-1-2+3-4+5-6-7+8-9-10+11+12 = 0
-1-2+3-4+5-6-7-8+9+10-11+12 = 0
-1-2+3-4-5+6+7-8-9-10+11+12 = 0
-1-2+3-4-5+6-7+8-9+10-11+12 = 0
-1-2+3-4-5+6-7-8+9+10+11-12 = 0
-1-2+3-4-5-6+7+8+9-10-11+12 = 0
-1-2+3-4-5-6+7+8-9+10+11-12 = 0
-1-2-3+4+5+6+7+8+9-10-11-12 = 0
-1-2-3+4+5-6+7-8-9-10+11+12 = 0
-1-2-3+4+5-6-7+8-9+10-11+12 = 0
-1-2-3+4+5-6-7-8+9+10+11-12 = 0
-1-2-3+4-5+6+7-8-9+10-11+12 = 0
-1-2-3+4-5+6-7+8+9-10-11+12 = 0
-1-2-3+4-5+6-7+8-9+10+11-12 = 0
-1-2-3+4-5-6+7+8+9-10+11-12 = 0
-1-2-3-4+5+6+7-8+9-10-11+12 = 0
-1-2-3-4+5+6+7-8-9+10+11-12 = 0
-1-2-3-4+5+6-7+8+9-10+11-12 = 0
-1-2-3-4+5-6+7+8+9+10-11-12 = 0
-1-2-3-4-5+6-7-8-9+10+11+12 = 0
-1-2-3-4-5-6+7-8+9-10+11+12 = 0
-1-2-3-4-5-6-7+8+9+10-11+12 = 0

（2）
1到12的数字和 = （1 + 12）*12/2 = 78
要使正号的数、负号的数和为0，那么正号的数绝对值 = 负号数的绝对值
也就是，加负号的数的和要等于 78/2 = 39
要使符号加的最少，必须尽量找大的数加：
39 = 12 + 11 + 10 + 6 至少等于4个数的和，不可能再少了。
因此负号至少需要添加4个。
例如：
1+2+3+4+5-6+7+8+9-10-11-12 = 0
1+2+3+4+5+6-7+8-9+10-11-12 = 0

Answer 2

1-2-3+4+5-6-7+8+9-10-11+12=0