MATHEMATICS TEACHING

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.) |

Note that 26, 27 28 and 29 have (black) holes in them.

25. |
26. |
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27. |
28. |
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29. |

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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