problem 32

"""
We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital.

The product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital.

Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital.

HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.
"""

digits = ['1', '2', '3', '4', '5', '6', '7', '8', '9']
def checked(N,M):
  d = str(N) + str(M) + str(N*M)
  d = sorted(d)
  if d == digits:
    return True
  return False


def has_duplicate_digits(num):
  return len(set(str(num))) != len(str(num))


W = set()
for a in range (1,999):
  if has_duplicate_digits(a):
    continue
  for b in range (a + 1,9999) :
    if has_duplicate_digits(b):
      continue
    if checked(a,b) :
      W.add(a*b)
print(sum(W))