Pentominoes

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

The Acme Tile company has observed a growing market for oddly shaped tiles, such as

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

Tiles of this form made up of five squares are called pentominoes. How many different shapes of pentominoes are there? What are they?


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