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## No. 1980: 2nd Birthday Special: Print, Cut Out, and Solve

First | Previous | 2014-10-20 | Next | Latest

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Strip by: Alien@System

{A square of picture fragments in different orientations}

The author writes:

Pentominoes are one of the "classics" among puzzles. Similar to tangram, the goal of such a puzzle is to recreate a given shape with the pieces available, without overlapping or gaps. The pieces, the titular pentominoes, are shapes consisting of 5 squares of the same size, joined edge to edge. Every piece is only present once, counting rotations and flipping, which leaves 12 unique pieces that are usually named after letters in the alphabet they more or less resemble.

One of the oldest challenges with those pieces was arranging them in a rectangle. As there are 12×5 = 60 squares overall, there are several possibilities of rectangles. One of them, 4×15, has been solved completely with the computer, so now we know that it has 368 unique solutions, which excludes simple rotations and reflections.

Another standard challenge was of course, since most puzzle solvers also like chess, to place the pieces on a chess board. Since that has 64 squares, four have to remain empty, traditionally the 4 centre ones, a configuration that has only 65 unique solutions. Interestingly, excluding a few configurations that trivially fail to work, any choice of four empty squares can be solved, although the number of solutions can of course be very limited.

Original strip: 1980-06-19.