Project Euler/32

Problem Statement

An n-digit number is pandigital if it makes use of all digits 1 to n exactly once

Example: the 5-digit number 15234 is pandigital for digits 1 thru 5

The product 7254 is pandigital, for digits 1 thru 9:

$ 39 \times 186 = 7254 $

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

Note that some products can be obtained in more than one way, so only include it once in the sum

Approach

Set the bounds for the multiplicand and multiplier:

(1 digit number) x (4 digit number) = (5 digit number)

In theory, search space will be all numbers up to 4 digits. In reality, can deduce the range of one number based on what we choose as the other number:

A x B = C

Let C = 10^6 (maximum 5-digit number)

Then if A is a 1-digit number, B ranges up to 10^5 (maximum 4-digit number)

If A is a 2-digit number, B ranges up to 10^4 (maximum 3-digit number)

etc...