New Scientist Enigma 1714 – Building Sand Castles

by Susan Denham

From Issue #1714, 28th April 1990

You can add a letter at a time to build up words from ‘A’ to ‘CASTLE’ in the following way:

A → AT → CAT → CAST → CASTE → CASTLE

Now I can substituted digits for letters in many ways, one being:

5 → 56 → 256 → 2576 → 25761 → 257631

in which there are numbers divisible by 2, by 3, by 5 … and in fact only the first number is prime.

Your task today is to find a different substitution of non-zero digits in that word-chain (as always different digits consistently replacing different letters) so that none of the resulting numbers is divisible by 2 or 3 or 5 — and in fact so that they are all prime and so that SANDS is prime too.

You don’t have to dig too hard — there are lots of short-cuts and, of course, there is an answer.

What is the value of CASTLE?