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MATHEMATICS TEACHING

PENTOMINOES
A Miscellany


23. Of the 12 pentominoes, which ones could be used as the net for making an open-topped box?
24. Find the smallest number of Y-pentominoes needed to fill a rectangle completely.
(It is less than 20.)
Make each of these shapes with a full set of 12 pentominoes.
Note that 26, 27 28 and 29 have (black) holes in them.
25. pentomino cross 1 26. pentomino cross 2
27. pentomino steps 28. pentomino triangle
29. pentomino grid

Solid pentominoes

If the pentominoes are made using cubes instead of squares then it becomes possible to work with 3-dimensional shapes.
The simplest problem then is to put all 12 together to make a cuboid. Clearly it will have a volume of 60 cubes.
It can be done as
a 3 by 4 by 5; or a 2 by 5 by 6; or a 2 by 3 by 10.
All of these are possible.

8 of the solid pentominoes can be assembled to make a twice-size representation of almost any one of them. This is NOT possible in the case the I, T, W and X.


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