undividable_clique.py

#!/usr/bin/env python3

from itertools import combinations


def is_undividable_clique(family, number):
    for subgraph in combinations(family, 4):
        if sum(subgraph) % number == 0:
            return False
    return True


number = 23
natural_number_set = range(1, number)


for size in range(4, number+1):
    print('now checking', size)
    for family in combinations(natural_number_set, size):
        if is_undividable_clique(family, number):
            break
    else:
        break
size -= 1
print(size)


families = []
ways = 0
for family in combinations(natural_number_set, size):
    if is_undividable_clique(family, number):
        ways += 1
        families += [family]
print(ways)

print(families[0])
print(families[-1])
print(max(families, key=sum))