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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?

The Mean Problem

Stage: 4 Challenge Level: Challenge Level:1

Start by thinking about what these two things together tell you :

"the mean of the first three was 9"

"the mean of all four was 15"