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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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Speedy Sidney

Two trains set off at the same time from each end of a single straight railway line. A very fast bee starts off in front of the first train and flies continuously back and forth between the two trains. How far does Sidney fly before he is squashed between the two trains?

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.