Question

从1 /2,1/3,1/4,1/5...1/90,1/91,这90个分数中选出10个加上正负号,使之和为-1.

Answer 1

解这种题,一般首先是找出满足结果的和,不管有多少组,然后剩下的可以通过对消得0.
-1/2-1/3-1/6=-1
还差7个数
1/4-(1/8+1/12+1/24)=0
1/10-(1/15+1/30)=0
=>-1/2-1/3-1/6-1/4+1/8+1/12+1/24-1/10+1/15+1/30=-1
1/8-(1/12+1/24)=0
1/5-(1/10+1/15+1/30)=0
=>-1/2-1/3-1/6-1/8+1/12+1/24-1/5+1/10+1/15+1/30=-1
1/6=1/4-1/12
1/7-(1/8+1/56)=0
1/9-(1/10+1/90)=0
=>-1/2-1/3-1/4+1/12-1/7+1/8+1/56-1/9+1/10+1/90=-1
.
更多的可以自己组合了