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 paint a polysquare by dropping a set of monochrome squares. The system will automatically change the colour of the tokens after you have completed painting one tile.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. (Note 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.)
Also try to find 'faultfree' solutions: Once you have solved a puzzle, try to solve it with the additional condition that the tiling shall be 'faultfree', i.e. it has no breaking line from one side of the border to the other.
There are also six 'Freeplay' options available from 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.
Several of the puzzles presented here have been taken from my book 'A Puzzling Journey To The Reptiles And Related Animals', 1986, one of three books on geometrical problems and puzzles I have privately published. For details see my web page.
Another good source for related problems is Solomon Golomb's book 'Polyominoes'.
More freeware as well as real puzzles and games at my homepage http://karl.kiwi.gen.nz. |
