Is the mean of the squares of two numbers greater than, or less
than, the square of their means?
Can you use the diagram to prove the AM-GM inequality?
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 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.