snape.py

from collections import defaultdict


def all_pairs():
    for n1 in range(2, 65):
        for n2 in range(n1+1, 65+1):
            yield n1, n2


def prod(pair):
    n1, n2 = pair
    return n1 * n2


def find_numbers():
    sum_to_pairs = defaultdict(list)
    prod_to_pairs = defaultdict(list)

    for pair in all_pairs():
        sum_to_pairs[sum(pair)].append(pair)
        prod_to_pairs[prod(pair)].append(pair)

    draco_cant_tell = set()
    for pair in all_pairs():
        num_options = len(prod_to_pairs[prod(pair)])
        if num_options > 1:
            draco_cant_tell.add(pair)
        assert num_options >= 1

    harry_can_tell_draco_cant_tell = set()
    for pair in draco_cant_tell:
        options = sum_to_pairs[sum(pair)]
        if all(p in draco_cant_tell for p in options):
            harry_can_tell_draco_cant_tell.add(pair)

    draco_can_now_tell = set()
    for pair in harry_can_tell_draco_cant_tell:
        options = [p for p in prod_to_pairs[prod(pair)] if p in harry_can_tell_draco_cant_tell]
        if len(options) == 1:
            draco_can_now_tell.add(options[0])

    harry_can_now_tell = set()
    for pair in draco_can_now_tell:
        options = [p for p in sum_to_pairs[sum(pair)] if p in draco_can_now_tell]
        if len(options) == 1:
            harry_can_now_tell.add(options[0])
            
    assert len(harry_can_now_tell) == 1, harry_can_now_tell
    (n1, n2), = harry_can_now_tell
    print(n1, n2)


if __name__ == '__main__':
    find_numbers()