Tetrominoes

[Based loosely on some problems in chapter 2 of Another Fine Math You've Got Me Into ... by Ian Stewart.]

Sam and Michelle Rebelsky have recently purchased a house and need to retile some rectangular and square floors. They visit the local Home Depot and discover that there are many shapes and sizes of tiles. They are particularly attracted to the tiles labeled "tetrominoes".

Here are the basic tetrominoes. Note that each one is made up of four squares.

+--+  +--+--+  +--+--+  +--+     +--+
|  |  |  |  |  |  |  |  |  |     |  |
|--|  +--+--+  +--+--+  +--+--+  +--+--+
|  |  |  |  |  |  |     |  |  |  |  |  |
|--|  +--+--+  +--+     +--+--+  +--+--+
|  |           |  |     |  |        |  |
+--+           +--+     +--+        +--+
|  |
+--+

What is the minimum number of each tetromino you need to completely tile a rectangle? A square? You cannot cut the tetrominoes.


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