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Programming Enigma Puzzles

6 October 2014

Posted by on **From New Scientist #1373, 1st September 1983** [link]

Another letters for numbers problem. It may leave you at sea, for it is a tease to keep you on your toes. You see, each letter stands for a

differentdigit each time it appears.What is a

TEASE?

**Note:** I am waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment. The latest estimate is that I’ll have a connection by the end of October 2014.

[enigma227]

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This Python program uses the

SubstitutedDivision()solver from theenigma.pylibrary to examine long division sums with the right “shape”. It runs in 390ms.Solution:TEASE = 58044.A similar program will work with the new version of the

SubstitutedDivision()solver in theenigma.pylibrary, although there are some minor differences (the intermediate subtraction sums are included directly in the returned solutions, but the new version does include empty intermediates, and we can also provide acheck()function to the solver, to select the required solution).Here is a version of the above program that works with the latest version of the

SubstitutedDivision()solver. It runs in 336ms.But using the

distinctparameter to the newSubstitutedDivision()solver (which is inherited from theSubstitutedExpression()solver) we can specify the collections of symbols that have to take on distinct values amongst their own group. I use lower case letters to stand for the symbols in the division sum, and then group together symbols that correspond to the same upper case letter in the puzzle statement.Instead of requiring a specialised program the puzzle can be solved by presenting the right arguments to the

SubstitutedDivision()solver. Here is the necessary run file. It executes in 113ms.