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Programming Enigma Puzzles

11 January 2017

Posted by on **From New Scientist #1136, 4th January 1979** [link]

Across:1. The sum of the digits is 10.

3. Digits all even.

4. Digits all odd, and each one is less than one before.

Down:1. The second digit is greater than either of the other two.

2. A multiple of 3 Down.

3. The second digit is greater than the first one.(One of these numbers is the same as another one reversed and there are no 0s).

This completes the archive of *New Scientist* puzzles published in 1979.

[puzzle84]

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There is a solver for crossfigure puzzles in the

enigma.pylibrary, but in this case it is faster to use the generalSubstitutedExpression()solver.In the following program the crossfigure puzzle is solved using the

SubstitutedExpression()solver, and then we inspect the answers to check that one answer is the reverse of one of the other answers.This Python program runs in 65ms

Solution:The completed cross figure puzzle is:The answer to 1 down is the reverse of the answer to 2 down (and vice versa, of course).

Without this condition there are 36 different solutions to the crossfigure puzzle.