Object: Fill the playing area with Y-pentominoes. (30 variants)
 
If a shape tiles a rectangle, then this rectangle is called a 'prime rectangle' or a 'prime' for short, if it is minimal in the sense that it cannot be cut into smaller rectangles which also can be tiled by the given shape.
 
Hence for each shape that is 'rectifiable' (i.e. which can tile a rectangle), it is an interesting task to find all prime rectangles ('primes') for this tile. For any given tile there can only be a finite number of such rectangles. For the Y-pentomino we present here all known prime rectangles small enough to fit onto our board of size 32x32.
 
The Y-pentomino is represented by five square tokens.The system will automatically change the colour of the tokens after you have put down 5 tokens.
 
The system guides you through the placing of the five tokens per tile: Place two squares side by side, then a third orthogonally next to the second. The system will drop the remaining two squares automatically.
 
You can DELETE a placed pentomino by simply clicking the three squares which you placed on the board when you created the tile.
 
You win if you manage to fill the given rectangle. Solutions (zsg files) for most variants are attached.
 
Please note that there are three piece sets available.
 
 
The primes 10x16, 15x16 and 15x22 were first published by C.J. Bouwkamp and D.A. Klarner in JRM(3(1), which used a computer.
The 15x15 prime was found by Jennifer Hazelgrove with a computer (see JRM 7(3)).
All other primes were found by hand (!) by the author (9x20, 9x30, 10x14, 11x20, 14x15, 17x30, 21x25, 25x27), see Journal of Recreational Mathematics Vol 12(3), 1979-80. Astonishingly, my results found by hand bettered some of the earlier results found by computer.
 
Some of my results on prime rectangles (10x23, 11x30, 17x30, 18x25, 21x25) are published with this Zillions game for the first time. (I had these results to JRM in 1980, but they did not publish them because of the amount of matarial they had published on that topic already).
 
In the later years Torsten Sillke investigated a lot in the area of primes in two and three dimensions, using a computer (http://www.mathematik.uni-bielefeld.de/~sillke/).
 
 
See also the Zillions games 'Pento', 'Ypento' and 'Reptiles' for related puzzles.
 
Background design : fractal T011001l by Karl Scherer.
 
More freeware as well as real puzzles and games at my homepage http://karl.kiwi.gen.nz.