Tetris in 3D with 5 units - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T14:02:59Z http://mathoverflow.net/feeds/question/13634 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/13634/tetris-in-3d-with-5-units Tetris in 3D with 5 units David 2010-02-01T08:04:56Z 2010-02-01T11:43:45Z <p><strong>Background:</strong> There are 7 "bricks" used in the game of Tetris. These are the 7 <em>unique</em> combinations of 4 unit squares in which every square shares at least one edge with another square. ("unique" in this case refers to the idea that no brick can be rotated in 2-D space to become another brick.)</p> <p><strong>Question:</strong> Using 5 unit cubes, how many <em>unique</em> "bricks" could be formed in which each cube shares at least one face with another cube? (Please provide a proof to this in your answer if you can find one.)</p> http://mathoverflow.net/questions/13634/tetris-in-3d-with-5-units/13659#13659 Answer by TonyK for Tetris in 3D with 5 units TonyK 2010-02-01T11:14:37Z 2010-02-01T11:14:37Z <p>There are 29 distinct 5-cube bricks (counting mirror images as distinct). Together with one 1-cube brick, one 2-cube brick, two 3-cube bricks, and eight 4-cube bricks, these constitute the brick set for the highly addictive 3-D Tetris game Blockout II, available at <a href="http://www.blockout.net/blockout2/" rel="nofollow">http://www.blockout.net/blockout2/</a>. Source code is also available.</p> <p>I think a proof just involves writing out the cases.</p>