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.View the archive of all weekly problems grouped by curriculum topic