The question (originally posed during the 70's in the magazine Games and Puzzles) is "What is the smallest polyomino that tessellates and locks?" The published solution was this, in which the polyomino has 25 squares.
It didn't look very minimal to me. I soon found one with 18 squares.
There's an easy simplification of that one that gets us down to 15 squares.
Much doodling later, I found this one that only uses 14 squares. As far as I know, this is the smallest known.
Unless, that is, you allow some of the polyominoes to be flipped over, when you can get away with as few as 12 squares - less than half the originally claimed minimum of 25!
Some of these polyominoes are given in The Penguin Dictionary of Curious and Interesting Geometry (ed. David Wells).
All of these backgrounds were produced using SAS DSGI software.
Please also take a look at Squaring the Square.
For some links to kindred sites, see my links page.
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This page last edited 12/12/2007