![[Information Index]](ico/objinfo.gif){kind=small}
![[Generation Index]](ico/objgen.gif){kind=small}
![[COS homepage]](ico/cos.gif){kind=small}
First, the 3 by 30 shape in text followed by a gif rendering.
VZIIIIITWYYYYNNNFfnnnzzllllXUU VZZZPPPTWWYLNNFFFffynnzlppXXXU VVVZPPTTTWWLLLLFffyyyyzzpppXUU
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More to come when I get some time....
Take a pentomino piece and increase its linear dimension by a factor of three. The resulting shape contains room for 9 pentomino pieces. The problem is to fill in the shape using pentomino pieces. It's known as the triplication problem, and is attributed to Raphael Robinson. There are 12 separate puzzles, one for each shape. Below we show a solution for the X piece, together with the three omitted pieces.
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COS can be coaxed into giving solutions to the triplication puzzle, but you have to decide which three pieces to omit, and place them in a region disjoint from the triplication shape. The diagram above shows the idea and is, in fact, extracted from a COS solution. Omitting the I, X, and W pieces works remarkably well in general.