# Requires Python 2.7 for latest itertools functions.

import itertools

allnums = [3,3,7,7]
# [3, 3, 7, '/', '+', 7, '*']   # RPN
#  == 3 + (3/7) * 7
#  == 24
allnums = [1,3,4,6]
# [6, 1, 3, 4, '/', '-', '/'])  # RPN
#  == 6 / (1 - (3/4))
#  == 24

target = 24

allops = {
    "+": (lambda a,b: a+b),
    "-": (lambda a,b: a-b),
    "*": (lambda a,b: a*b),
    # Convert to floating point (and use epilson for comparison below) to
    # allow (approximate) fractional calculation.
    "/": (lambda a,b: float(a)/b),
}

def rpncalc(input):
    stack = []
    for i in input:
        if isinstance(i, str):  # op
            try:
                b, a = stack.pop(), stack.pop()
            except IndexError:
                result = "illegal"
                break
            try:
                stack.append(allops[i](a, b))
            except ZeroDivisionError:
                result = "NaN"
                break
        else:
            stack.append(i)
    else:
        result = stack[-1]
    return result

def doit():
    numperms = set()
    for perm in itertools.permutations(allnums, 4):
        if perm in numperms:
            continue
        numperms.add(perm)
    results = set()
    for opnames in itertools.product(allops.keys(), repeat=3):
        for nums in numperms:
            # This permutations isn't quite right: creates dupes in the whole
            # set because we've already done the other orders.
            for ordering in itertools.permutations(nums[2:] + opnames[:-1]):
                input = list(nums[:2])
                input += ordering
                input.append(opnames[-1])
                result = rpncalc(input)
                if not isinstance(result, (int, float)):
                    pass
                else:
                    print "rpncalc(%s) = %s" % (input, result)
                    results.add(result)
                    if abs(target - result) < 0.1:  # epsilon
                        print "Found it!"
                        return
    print sorted(results)

doit()