How many ways can a 3x4 rectangle be cut into two polyominoes by cutting along the grid lines? (Not counting reflections and rotations.)
Examples of valid cuts are shown in the first row and invalid cuts are shown in the second row:

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

+--+--+--+--+   +--+--+--+--+   +--+--+--+--+   +--+--+--+--+
|     |     |   |           |   |  |        |   |     /     |
+  +  +  +  +   +--+--+  +  +   +  +  +--+  +   +  + /+  +  +
|     |     |   |  |  |     |   |        |  |   |   /       |
+--+--+  +  +   +  +--+  +  +   +  +--+--+  +   +  +  +  +  +
|     |     |   |           |   |     |     |   |  |        |
+--+--+--+--+   +--+--+--+--+   +--+--+--+--+   +--+--+--+--+

(In reply to re: Solution missed some by Jer)

Just happened to look at this with Internet explorer 6.0. Two breaks in a row come out as only one line break, so all the solutions merge together.  Looks as intended using Firefox.

Posted by Charlie on 2007-12-07 15:59:47