I'm trying to work out a puzzle I came up with related to Tetris. I want to come up with a way to use the 7 Tetris blocks ( http://en.wikipedia.org/wiki/Tetris#Gameplay ) to fill up a square surface without any gaps. Here are the rules: 1. Tetrads - Can only use the 7 Tetris shapes, and there can be no gaps or holes. 2. Square - The surface has to be a square. 3. Size - The square can be any size between 7x7 through 20x20. 10x10 would be good though. 4. Neighbors - No block can touch another block of the same type. IE, you can't fill the space with 2x2 O tiles. Diagonal corner touching is OK though. 5. Blocks - If the finished block is copied and put on any of the 4 sides of the first block, rule #4 still applies. EG, you can't have a 2x2 O shape at the bottom right and bottom left of the block, since if the whole block is copied to the right, the 2 shapes would be touching. Obviously, #5 is the kicker! The created block has to be able to be used to fill up a larger grid of blocks and still hold to rule #4. Here is an example of an 8x8 grid, but it breaks rules #4 and #5 since the same type of tetrads are touching (even though they are different colors) http://blog.craftzine.com/TetrisBlanket.jpg Example of a 6x6 grid, also breaking rules 4 and 5: http://daddytypes.com/archive/oguro_tet ... blocks.jpg 8x5 grid, breaks rules 4 and 5, and 2 since it's a rectangle: http://www.inhabitat.com/images/tetris_new_big.jpg Here is one that is closer. It is a 10x10 grid that actually tessellates to fill up a larger space (set it to your desktop wallpaper to see). It is close to fulfilling rules 4 and 5. But it breaks #1 since the square itself has gaps or cut off tetrad shapes. http://art1.server05.sheezyart.com/medium/75/754773.jpg And here's an example of a larger number of blocks covering a large space without gaps, but obvious breaking rule #2. But it fulfills rule #4! http://i61.photobucket.com/albums/h44/d ... lpaper.jpg Also check out Tetris Tiles for ideas: http://www.tetris-tiles.com/ Alright, I know this is a tall order. But I'm hoping that some experts here on this forum would know about some solutions to this already, or be able to come up with a solution or prove that it is impossible!