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Programming Enigma Puzzles

2 October 2014

Posted by on **From New Scientist #1372, 25th August 1983** [link]

In the following fully-worked division, all the digits have been replaced by blanks except for one. And before you start counting your blessings in having at least one digit to go on, I must tell you that the 5 is, in fact, wrong.

What is the five-digit quotient?

**Note:** I am still waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment.

[enigma226]

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This Python program uses the [[

`SubstitutedDivision()`

]] solver from theenigma.pylibrary. It runs in 699ms.Solution:The quotient is 2.1875.The new [[

`SubstitutedDivision()`

]] solver in theenigma.pylibrary is derived from the [[`SubstitutedExpression()`

]] solver, so can use the same solver parameters that it does. This means that we can provide the condition that the digit specified is not 5 directly to the solver, rather than reject general solutions where it does stand for 5 at the end.Here is a run file problem that executes in 259ms.