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"""
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.
"""
import itertools
def isCombinationValid(combination):
"""
Checks if a combination (a tuple of 9 digits)
is a valid product equation.
>>> isCombinationValid(('3', '9', '1', '8', '6', '7', '2', '5', '4'))
True
>>> isCombinationValid(('1', '2', '3', '4', '5', '6', '7', '8', '9'))
False
"""
return (
int("".join(combination[0:2])) * int("".join(combination[2:5]))
== int("".join(combination[5:9]))
) or (
int("".join(combination[0])) * int("".join(combination[1:5]))
== int("".join(combination[5:9]))
)
def solution():
"""
Finds the sum of all products whose multiplicand/multiplier/product identity
can be written as a 1 through 9 pandigital
>>> solution()
45228
"""
return sum(
set(
[
int("".join(pandigital[5:9]))
for pandigital in itertools.permutations("123456789")
if isCombinationValid(pandigital)
]
)
)
if __name__ == "__main__":
print(solution())