gistfile1.txt

def add(x, y):
	ml = max(len(str(x)), len(str(y)))
	x, y = str(x).zfill(ml + 1), str(y).zfill(ml + 1)
	carries = 0
	z = ""
	carry = 0
	for a, b in zip(map(int, x[::-1]), map(int, y[::-1])):
		c = a + b + carry
		if c >= 10:
			carries += 1
			carry = 1
		else:
			carry = 0
		z = str(c % 10) + z
	return (carries, int(z))

def verify(start, sums):
	start = start[:]
	carries = 0
	for x, y in sums:
		if x == y:
			if start.count(x) < 2:
				print(start, x, y)
				return False
		else:
			if x not in start or y not in start:
				print(start, x, y)
				return False
		c, t = add(x, y)
		carries += c
		start.remove(x)
		start.remove(y)
		start.append(t)
	return carries

def summations(a):
	if len(a) == 2: return [[(a[0], a[1])]]
	sums = []
	for i in range(len(a)):
		x = a[i]
		for j in range(i + 1, len(a)):
			y = a[j]
			for ss in summations(a[:i] + a[i + 1:j] + a[j + 1:] + [x + y]):
				sums.append([(x, y)] + ss)
	return sums

import random

a = [random.randint(1, 100) for _ in range(7)]

ss = summations(a)

t = set()

for s in summations(a):
	v = verify(a, s)
	t.add(v)
	if v is False:
		print(a, s)

print(t)