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Programming Enigma Puzzles

8 October 2018

Posted by on **From New Scientist #1620, 7th July 1988** [link]

I have an ordinary set of 28 dominoes, but I’ve painted over the numbers. I’ve left the blanks alone and painted E’s over the 1’s, N’s over the 2’s, I’s over the 3’s, G’s over the 4’s, M’s over the 5’s and A’s over the 6’s.

My nephew was playing with the dominoes and managed to arrange 18 of them, some “horizontal” and some “vertical”, so that the letters and blanks were in the positions shown.

I forgot which letters were in the positions marked “?” but I remember that all four “?”s were the same, and no two were on the same domino.

Which letter is “?” and how many of the 18 dominoes were “horizontal”.

[enigma469]

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This Python 3 program runs in 130ms.

Run:[ @repl.it ]Solution:The squares marked with “?” should be “I”. There are 6 horizontal dominoes.There is only one layout that satisfies all the conditions:

Without the condition that there can’t be two “unknowns” on the same domino there is a further solution with 8 horizontal dominoes.