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.

(1) There are thirty triplets for part 1.  Will list later.

124 125 129 136 138 146 148 149 159 167

178 234 248 256 257 258 269 279 289 345

347 349 356 368 468 489 569 579 589 678

(Addendum:)

For part (2) -- four digits, diviser test 23 -- , I get 40 lines (from 1,2,3,4 to 3,7,8,9).  I'll check other postings before listing all of these.

Edited on November 8, 2010, 2:26 pm

Edited on November 8, 2010, 5:43 pm

Posted by ed bottemiller on 2010-11-08 13:24:24