这是一个小学生奥数题
使用python解：

一种方式，使用全排列方式找出

import itertools

ops = [["+","-",""]]*8

eightops=list(itertools.product(*ops))

snum=[str(i) for i in range(1,10)]
k=0
for i in range(len(eightops)):
    xch = snum[0]
    for j in range(8):
        xch = xch + eightops[i][j] + snum[j+1]
    if eval(xch) == 100 :
        k = k + 1
        print(f"{k:<5}{xch}")
    if eval("-" + xch) == 100:
        k = k + 1
        print(f"{k:<5}-{xch}")

一种方式，使用回溯组合的方式：

i = 1
def sum_for_100(pattern):
    global i
    if len(pattern) == 17:
        try:
            e = ''.join(pattern)
            if eval(e) == 100 :
                print(i, e)
                i=i+1
            if eval("-" + e) == 100:
                print(i, "-" + e)
                i=i+1
        except Exception as e:
            pass
    else:
        x = int(pattern[-1])
        for czf in ['+','-','']:
            pattern.append(czf)
            pattern.append(str(x + 1))
            sum_for_100(pattern)
            pattern.pop(-1)
            pattern.pop(-1)

sum_for_100(['1'])

哪种更好呢?