Peter And Sandy

peter_knows.py

from collections import defaultdict

# build pairs
pairs = []

for i in range(1, 100):
    for j in range(i, 100):
        pairs.append((i, j))


def singles_operation(f):
    results = defaultdict(list)
    for a, b in pairs:
        results[f(a, b)].append((a, b))

    singles = []
    for value in results.itervalues():
        # We want to return only the product/sum with one result because if
        #   peter/sandy have this product/sum, then they'll know the two numbers
        if len(value) == 1:
            singles.append(value[0])

    # Sorted for readability
    return sorted(singles, key=lambda x: x[0])


def remove_products():
    singles = singles_operation(lambda x, y: x * y)

    print 'peter removed', singles
    for s in singles:
        pairs.remove(s)

def remove_sums():
    singles = singles_operation(lambda x, y: x + y)

    print 'sandy removed', singles
    for s in singles:
        pairs.remove(s)

for i in range(7):
    remove_products()
    remove_sums()

# This is the result because it returns the only pair with a product
#   not created by anything else left in the list.
print 'result', singles_operation(lambda x, y: x * y)