"""
There are 31 different animals and we want to have a deck of cards such that on each card there are 6 animals and every card has exactly one animal in common with every other card. Our card deck should have at least 30 cards.
"""

from itertools import combinations
from random import shuffle
from pprint import pprint

n_animals = 31
n_animals_per_card = 6

print(
    "number of possible combinations:",
    len(list(combinations(range(n_animals), n_animals_per_card))),
)

decks = []
cards = []
while len(cards) < 30:

    combs = list(combinations(range(n_animals), n_animals_per_card))
    shuffle(combs)

    cards = [set(combs[0])]

    for combination in combs:
        valid_comb = True
        combination_set = set(combination)
        for card in cards:
            if not len(card.intersection(combination_set)) == 1:
                valid_comb = False
                break
        if valid_comb:
            cards.append(combination_set)

    cards = [list(card) for card in cards]
    print("size of current carddeck:", len(cards))

    decks.append(cards)
pprint(decks[-1])