Find the smallest whole number N such that N^3 is the product of three distinct 10-digit pandigital numbers A, B, and C.

(x)(2x)(4x) = 8x^3 = (2x)^3
So any pandigital that when doubled and quadrupled is still a 10-digit pandigital will solve the problem.
It turns out this holds true for the smallest pandigital 1023456789
1023456789*2046913578*4093827156 = 2046913578^2
So N = 2046913578 works, though maybe not the smallest.  But we don't need to consider N values greater than this.

We also don't need to consider pandigital values greater than 8187654240, because
2046913578^3 / (smallest pandigital * second smallest pandigital) is about 8187654240.  This shortens the list of pandigitals by about 20%

Posted by Larry on 2023-10-29 11:03:15