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.

(In reply to re: computer solution by Ady TZIDON)

It doesn't work with 5 digits and 7 (or 23) (i.e., no results).

It does work with 11 however:

1  2  3  4  5
1  2  4  5  7
1  2  5  6  7
1  2  6  7  8
1  2  6  8  9
1  3  4  5  9
1  3  4  6  9
1  3  4  7  8
1  3  5  7  9
1  3  6  8  9
1  3  7  8  9
1  4  5  7  8
1  4  5  8  9
2  3  5  6  7
2  3  5  6  8
2  3  5  7  9
2  4  5  7  9
2  4  6  7  9
2  4  6  8  9
3  5  6  8  9
4  5  6  8  9

and with 31:

1  3  4  6  8
2  4  5  7  8
3  4  7  8  9

Posted by Charlie on 2010-11-09 03:00:20