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Programming Enigma Puzzles

4 February 2013

Posted by on **From New Scientist #2627, 27th October 2007**

I have just made up a small crossword for our local newspaper. It is a square grid of traditional style with fewer than a quarter of the small squares shaded and the rest to be filled by “across” and “down” answers. The pattern of shaded squares has “180° symmetry”, i.e. if you rotate it through 180° about its central point, the layout looks the same.

The lengths of the answers, in the usual crossword order, are:

Across: 3 5 3 3 3 3 3 5 3

Down: 6 3 7 7 6 3and two of the answers are CROSSED and WORDS.

(a) What is the size of the grid (e.g. 11 by 11)?

(b) What are the clue numbers for ‘CROSSED’ and ‘WORDS’ (e.g. 6 Down and 12 Across)?

[enigma1466]

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The following Python program runs in 1.5s (under PyPy) and produces partially filled out grid.

Solution:(a) the grid is 7×7; (b) CROSSED is the solution to 3 Down, and WORDS is the solution to 5 Across.Here’s an image of the partially filled out crossword.

Filling in the remaining answers is left as a simple exercise for the reader.