**Background:** There are 7 "bricks" used in the game of Tetris. These are the 7 *unique* 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.)

**Question:** Using 5 unit cubes, how many *unique* "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.)