# Statement

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.

# Solution

The key to solve this problem is using a language like Python and determining when to stop processing.

When do we have to stop? Well, in order not to repeat multiplications I always use that the multiplier

is greater than the multiplicand. We will increase the multiplicand until the length of the string

"multiplicand/multiplier/product" is greater or equal 10, just then we increase the multiplicand.

And we stop the algorithm when the string "multiplicand/multiplicand/multiplicand * multiplicand" is

greater or equal to 10.

from CommonFunctions import is_pandigital if __name__ == '__main__': result = set() x = 2 while len(str(x) * 2 + str(x ** 2)) <= 9: y = x + 1 while len(str(x) + str(y) + str(x * y)) <= 9: if (x * y) not in result and is_pandigital(str(x) + str(y) + str(x * y)): result.add(x * y) y += 1 x += 1 result = sum(result) print("The result is:", result)

The Python file is available for download here.