问题若有1,2,3,…,n共n个数字,不改变它们的顺序,能否在每两个数字之间添上“+”或“-”号,使它们的和为0?当数字不多时,通过观察、计算,我们可以确定可否做到;当数字为4的倍数个时,我们由经验“1-2-3+4=0”、“5-6-7+8=0”得知,把它们自1起,每四个一组,符号依次为“+、-、-、+”即可.但问题又来了,当数字很多或数字不是4的倍数个时,还能做到吗?为叙述方便,我们把在1,2,3,…n的每两个 If the question has 1, 2, 3, ..., n a total of n numbers, without changing their order, can add “+ ” or “-” sign between every two numbers so that their sum 0? When the number is small, by observing, calculating, we can determine whether it can be done; when the number is a multiple of 4, we experience by “1-2-3 +4 = 0 ”, “5- 6-7 + 8 = 0 ”to know, put them from the beginning, every four groups, followed by symbols“ +, -, -, + ”But then the problem came again, when the number of many Or when the number is not a multiple of 4, can we still do it? For ease of narration, we put every two