Object: A shape which tiles a larger version of itself is called a rep-tile (from 'repetition tiling').
 
The selection screen offers you a choice of polysquares. Select a polysquare to start the corresponding game. The puzzle will show you that the polysquare is a rep-tile.
 
You have to fill the given area with copies of this tile. Mirror images are allowed. The given area is an enlarged version of the given polysquare or a rectangle.
 
You easily paint a polysquare by dropping only three squares, details see game text. The system will automatically drop all other squares. Details see game text. You can also easily delete a placed tile; see game descriptions.
 
You win if you manage to tile the given area.
 
For further details please consult the game descriptions and the history texts of the various games. Some solutions (zsg files) are included. (Note that each polysquare game has more than one variant associated with it. Especially there is a 'freeplay' variant on a big 32x32 board for each tile.)
 
There are also six 'Freeplay' options available on the main screen. In those games you may place the squares anywhere on the board. The colour of the squares will change automatically, e.g. in 'Freeplay 4' the colour of the dropped squares will change every 4 drops. This allows you to invent your own polysquares and to mix several types of polysquares.
 
Please note that there are three alternative piece sets available.
 
 
Good sources for related puzzles and problems are the following books:
Solomon Golomb's : 'Polyominoes', 1965 and 1994.
Karl Scherer : 'A Puzzling Journey To The Reptiles And Related Animals', privately published 1986.
 
Many people have worked on polyominoes in recent years, but of limitations of publishing space not very many solutions have been published (see my comments in game 'Y-primes').
 
Outstanding is the work of Torsten Sillke, who investigated a lot in the area of polysquares in two and three dimensions.He found hundreds of new rectangular packings using a computer. The condensed information on these results are available on his web pages. (http://www.mathematik.uni-bielefeld.de/~sillke/).The actual images of solutions, however, are still mostly unpublished...
 
More freeware as well as real puzzles and games at my homepage http://karl.kiwi.gen.nz.