## Teaser 2938: Numerophobia

**From The Sunday Times, 13th January 2019** [link]

In Letterland there are no numerals. They use the decimal system of counting just like we do but the digits 0-9 are represented by the first ten letters of the alphabet

A–Jinclusive but in no particular order. The following calculations are typical:

A + G = C

B × J = FH

GE × AI = HDBWhat number is represented by

ABCDEFGHIJ?

As stated this puzzle does not have a unique solution.

[teaser2938]

## Jim Randell 8:07 am

on8 March 2019 Permalink |We can feed the alphametic expressions directly to the [[

`SubstitutedExpression()`

]] solver from theenigma.pylibrary.This run-file executes in 125ms.

Run:[ @repl.it ]Solution:There are two solutions: ABCDEFGHIJ = 1840253697, and ABCDEFGHIJ = 3840951627.The two solutions arise as we can swap the values of (A, E) with (G, I). One of them is (1, 2) and the other is (3, 9).

Apparently the setter was unaware that there were two solutions, which seems a bit odd as this kind of puzzle can very easily be checked. For example my own alphametic solver is available here [ https://repl.it/@jim_r/alphametic ]. Click “Run”, enter the expressions, and you get the two solutions straight away.

Here’s an example transcript:

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## GeoffR 1:20 pm

on8 March 2019 Permalink |LikeLike