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Paving the Way

A man paved a square courtyard and then decided that it was too small. He took up the tiles, bought 100 more and used them to pave another square courtyard. How many tiles did he use altogether?

Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

Chess

What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?

Dissect

Age 11 to 14 Challenge Level:

The minimum number of squares a 13 by 13 square can be dissected into is 11:

There is one trivial solution to the size of the smallest square which can be dissected into squares which are all different sizes: the unit square! The smallest non-unit square which can be dissected into squares which are all different sizes has sides of length 175 units.

For further information on this and other similar problems see Chapter 11, Mrs. Perkins Quilt and Other Square-Packing Problems in Mathematical Carnival by Martin Gardner, published by Pelican books.