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Programming Enigma Puzzles

15 July 2013

Posted by on **From New Scientist #2572, 7th October 2006**

I have a five-digit TOTAL, a six-digit AMOUNT, and several other whole numbers, all expressed in words written in capital letters, where different letters stand for different digits and the same letter stands for the same digit.

A few curious properties are noticeable. For instance, if you add ANY amount to my TOTAL, and then divide by say, A value, the result is a whole number.

And if you subtract AN amount from my AMOUNT then divide by say, ANY value, the result, of course, is ANY amount.

How much is my five-digit VALUE?

There are now 457 *Enigma* puzzles up on the site – which means there are *only* 1300 “Classic” puzzles remaining to publish!

[enigma1412]

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This Python program runs in 34ms. It takes a different approach to the problem than the solution I coded up in Perl when the puzzle was originally published and is much faster.

Solution:VALUE = 89140.A simple, short permutation solution, but with a longer run time :

We can use the general Alphametic solver (

SubstitutedExpression()) from theenigma.pylibrary to solve this.Here is the command and it’s output. Overall run time is 71ms.

Or you can put the expressions in a file and just tell

enigma.pyto run it: