No matter how we permute the 3 digits 1,2 4 , none of the 6 three- digit numbers (124,142,214,241,412,421) is a multiple of 7.
Clearly, out of 84 possible triplets created by choosing distinct non-zero digits
there must be several like this, i.e. generating a 6-pack of three-digit numbers,
non divisible by 7.
1. List those triplets.
2. Similar question re:4 digits and divisibility by 23.