problem032.py

"""
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.
"""

from itertools import count
from math import log10


def digits_in(number):
    """
    >>> digits_in(1)
    1
    >>> digits_in(10)
    2
    >>> digits_in(111)
    3
    """
    return int(log10(number)) + 1


def main():
    """
    >>> main()
    45228
    """
    base = frozenset(["1", "2", "3", "4", "5", "6", "7", "8", "9"])

    products = set([])
    for x in range(2, 80):
        for y in count(x + 1):
            z = x * y

            # is the count of digits not above 9
            if digits_in(x) + digits_in(y) + digits_in(z) > 9:
                # can't be 1 trough 9 pandigital with more than 9 digits
                break

            # is x, y and z combind pandigital
            if base.issubset(str(x) + str(y) + str(z)):
                products.add(z)

    print(sum(products))


if __name__ == "__main__":
    import doctest
    doctest.testmod()