Solution for the sum product puzzle

sumproduct.py

answers = set()
MAX = 100
for a in xrange(2, MAX):
    for b in xrange(a, MAX):
        answers.add((a, b))

print len(answers)

# sum knows product doesn't know the answer so potential a, b can't have one product solution
products = {}
sums = {}
for a, b in answers:
    sums.setdefault(a + b, set())
    sums[a + b].add((a, b))
    products.setdefault(a * b, set())
    products[a * b].add((a, b))

potential_sums = set()
for (s, values) in sums.iteritems():
    allowed = True
    for a, b in values:
        if len(products.get(a * b, [])) == 1:
            allowed = False
    if allowed:
        potential_sums.add(s)

answers = filter(lambda (a, b): a + b in potential_sums, answers)
print len(answers)

# of the remaining solutions if there is only one product then product would know the answer
# since product knows the answer then the solution must have == 1 product
products = {}
for a, b in answers:
    products.setdefault(a * b, set())
    products[a * b].add((a, b))

answers = filter(lambda (a, b): len(products.get(a * b, [])) == 1, answers)
print len(answers)

# of the remaining solutions if there is only one sum then sum would know the answer
# since sum does know the answer then the solution must have == 1 sum
sums = {}
for a, b in answers:
    sums.setdefault(a + b, set())
    sums[a + b].add((a, b))

answers = filter(lambda (a, b): len(sums.get(a + b, [])) == 1, answers)
print len(answers)

print answers