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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Pythagorean Triples

How many right-angled triangles are there with sides that are all integers less than 100 units?

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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?

Red or Black

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

CubeEach edge of the cube borders borders two faces. As there are six faces, a minimum of three black edges will be required.


The diagram on the right shows that three black edges is enough.

 

This problem is taken from the UKMT Mathematical Challenges.