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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?
Age 11 to 14 Short Challenge Level:
The diagram shows a square within a square within a square within a square. Find the fraction of the area that is shaded.
This problem is taken from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.