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 15x4 - 368 solutions.
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!