from itertools import product
from collections import defaultdict

def gen_all_combos(part_sum, numbers_left, history=None):
    combos = product("+-*/", numbers_left)
    if not history:
        history = str(part_sum)
    for combo in combos:
        numbers_left_copy = list(numbers_left[:])
        numbers_left_copy.remove(combo[1])
        calc_string = history+''.join(map(str,combo))
        result = eval(calc_string)
        if result < 0 or abs(int(result)-result) > 1e-6:
            continue
        yield int(result), numbers_left_copy, '('+calc_string+')'

NUMBERS = [25, 75, 10, 7, 5, 4]
TARGET = 459
solutions = defaultdict(set)
for num in NUMBERS:
    nums = NUMBERS[:]
    nums.remove(num)
    for c1 in gen_all_combos(num, nums):
        solutions[c1[0]].add(c1[2])
        for c2 in gen_all_combos(*c1):
            solutions[c2[0]].add(c2[2])
            for c3 in gen_all_combos(*c2):
                solutions[c3[0]].add(c3[2])
                for c4 in gen_all_combos(*c3):
                    solutions[c4[0]].add(c4[2])
                    for c5 in gen_all_combos(*c4):
                        solutions[c5[0]].add(c5[2])
                        for c6 in gen_all_combos(*c5):
                            solutions[c6[0]].add(c6[2])
print(solutions[459])