You may also like

problem icon

Square Mean

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

problem icon


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

problem icon

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: Challenge Level:1

The sum of all $64$ numbers is their mean times the number of numbers, which is $64 \times 64 = 4096$. Similarly the sum of the first $36$ numbers is $36^2 = 1296$. Therefore the sum of the last $28$ numbers is $64^2-36^2= 4096 - 1296 = 2800$. Therefore the mean of the last $28$ numbers is $\frac{2800}{28}=100$.

This problem is taken from the UKMT Mathematical Challenges.