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Programming Enigma Puzzles

7 February 2013

Posted by on **From New Scientist #1197, 6th March 1980** [link]

“Cut the figure to make two identical parts” is a problem put in

100 Geometric Games, by Pierre Berloquin, which I have been reading. Having done so — not without difficulty — I looked up the solution and found it was quite different from mine.Interpreting “identical” as including “identical when turned over”, how many ways can

youfind of cutting the figure into two identical parts?

[enigma54]

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This is one that I’ve not been able to fully solve programatically in a satisfactory way. But by considering a simplified version of the problem I am able to find the required solutions in a reasonable time.

The following Python program assumes that the cut divides the figure along the grid lines shown in to two contiguous pieces, and further instead of considering the full 10×6 grid (48 squares) it considers a scaled down 5×3 grid (12 squares). Any solution thus found can obviously be scaled up to become a solution of the original problem. This program runs in 41ms.

Solution:There are three different ways.There is also a solution that uses non-contiguous regions.

I’ve played with some variations on the above program to attempt the more general problem, but the best I’ve come up with is a program to analyse possible cuts along the grid lines. On the 10×6 grid it examined 34,885,420 cuts in 5h37m, and found the same (contiguous) solutions given above.