some homework assignment for some freshman kid on reddit.

homework.py

# Given a list of numbers, write in increasing order all the integers you can
# obtain using each number once and any combination of addition,
# multiplication, division, and subtraction.
from itertools import permutations, product
from operator import add, mul, div, sub
solutions = set()
funcs = [add, mul, div, sub]
seeds = [22,71,13,1]

def polish(tokens):
    stack = []
    for token in tokens:
        if callable(token):
            stack.append(token(stack.pop(), stack.pop()))
        else:
            stack.append(token)
    return stack[0]

for operators in product(funcs, repeat=len(seeds)-1):
    for tokens in permutations(seeds + list(operators)):
        try:
            solutions.add(polish(tokens))
        except (IndexError, ZeroDivisionError):
            pass

print sorted(solutions)

a token list will raide an IndexError if the ordering isn't right, e.g., if you say 1 1 + + + 2 2 it's invalid. You get a ZeroDivisionError if you... divide by zero.