# Sunday Times Teaser 2626 – Homophones

### by Graham Smithers

Using different digits to consistently represent different letters, I have three primes, TWO, TOO and TO, and two further numbers, STRAIGHT and STRAIT, the digits of which form a consecutive set.

All numbers mentioned (including WOE below) have non-zero leading digits.

What number does WOE represent?

Here is my solution

and here is a much faster version that relies on a small amount of analysis

Another version – this gives all solutions and constant values for WOE,TWO,TOO and TO, plus variable values for STRAIT and STRAIGHT.

2. Here’s another one:

Hi Arthur,

Thank you for contributing here!

I noticed that, since O is the units digit of a three digit prime, it has to be odd so some of your (W,O) conditions aren’t necessary.

Also, are you sure that you have covered all possibilities when (W,O) comparisons are list rather than set based? I get:

E | ordered (W, O) values
0 | (1, 9), (2, 1), (8, 9), (9, 1)
7 | (8, 9)
8 | (7, 9), (9, 7)
9 | (8, 7)

Fortunately the ambiguous (8, 9) doesn’t occur 🙂