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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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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?

Square Bisection

Age 11 to 14 Short Challenge Level:

Any line which passes though the centre of the square divides the square into two congruent shapes. An example is shown below.

Figure 1

There are an infinite number of suitable lines (lines passing through the centre, at any angle) so there are infinitely many ways the square can be cut in half with a single straight cut.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.