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More about pentominoes

We could use a normal chessboard to play this interesting puzzle: there are 64 boxes, then we could cover the chessboard, except 4 holes, like the following picture. There are solutions for each position of the four holes. The symmetries are more interesting.


On this chessboard we could play a good strategy game for two players: each player in his turn places a pentomino on the chessboard, in the position that he thinks more convenient; the first who is not able to arrange his pentomino loose.

Now we show any rectangular boxes with area = 60. All the boxes have solutions.

Box 12x5

Box 12x5

Box 15x4

Box 15x4 - 368 solutions.

Box 3x20

Box 3x20 - 2 solutions only.

In the next game you must build a pentomino, magnified three times, by nine pentominoes. There are solutions for every pentominoes.



And now, ladies and gentlemen, an enigmatic question: 'Could you cover a cube, which has the edge equal to square root of 10, with the twelve pentominoes?' I hope you rack your brains before look at the SOLUTION!



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