Pentomino Problem


after Martin Gardner

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Puzzle 1. Twelve pentominoes are arranged in a 6x10 rectangle as is shown in the topmost diagram. Can you divide the rectangle, along the black lines only, into two parts that can be fitted together again to make the three-holed rectangle shown in the bottom diagram?

Puzzle 2. Arrange the twelve pentominoes to form a 6x10 rectangle but in such a way that each pentomino touches the border of the rectangle. Of the several thousand fundamentally different ways of making the 6x10 rectangle (rotations and reflections are not considered different), only two are known to meet the condition of this problem. Asymmetrical pieces may be flipped over.

Posted: July 26, 2008
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