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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 possible to dissect any square drawn on a grid into smaller squares, by cutting along grid lines.


For example a 3 by 3 square can be dissected into either 9 smaller squares or 6 squares:



  • What is the minimum number of squares a 13 by 13 square can be dissected into?
     
  • What is the smallest size square which can be dissected into squares which are all different sizes?