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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?

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Square Areas

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

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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:

It is certainly worthwhile looking at gradually increasing the size of the squares. With younger pupils it would be good to allow them to discuss the situation for even sided squares and those with a side that is a multiple of 3. For older/more able pupils its a good idea to go at least as far as a 43 by 43 square! When a large number have been tried I would suggest that pupils try to examine their "system" for getting the least number of squares.