### Square Mean

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

### AMGM

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

### 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?

# Partial Means

##### Stage: 4 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

The mean of a sequence of $64$ numbers is $64$. The mean of the first $36$ numbers is $36$. What is the mean of the last $28$ numbers?

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.