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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() |
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