**From New Scientist #2146, 8th August 1998** [link]

Throughout the following equations each letter stands consistently for either a non-zero digit or for one of the arithmetic symbols ×, ÷, + and –, with different letters being used for different symbols/digits.

When you have substituted the digits and symbols both equations make sense working from left to right (so that, for example, 5 – 2 × 23 = ((5 – 2) × 23) = 69), are correct, and, as our title implies, a + features somewhere.

AN = ENIGMA

ADDIT = UP

Find the value of AND.

[enigma991]

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Considering the expression:

Imust be an operator (asDcannot be – we can’t have two operators next to each other), so the expression is one of:We can immediately see that + and × are not going to give a 2-digit result, which means that the + must be in the other expression, so the two expressions are one of:

Applying the operations from left-to-right we get:

where

Mis +, andIis – or ÷.This Python program uses the [[

`SubstitutedExpression()`

]] solver from theenigma.pylibrary to try both options. It runs in 101ms.Run:[ @repl.it ]Solution:AND = 187.The expressions are: