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Square Mean

Is the mean of the squares of two numbers greater than, or less than, the square of their means?

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Can you use the diagram to prove the AM-GM inequality?

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Cubic Rotations

There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?

Tyneside Average Speed

Stage: 4 Short Challenge Level: Challenge Level:1

A van travels from Newcastle to South Shields at an average speed of 30 mph and returns by the same route at an average speed of 40 mph. What is the van's average speed for the whole journey?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.
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