You may also like

problem icon


This activity investigates how you might make squares and pentominoes from Polydron.

problem icon

Multilink Cubes

If you had 36 cubes, what different cuboids could you make?

problem icon

Cereal Packets

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Unequal Exam

Stage: 2 and 3 Short Challenge Level: Challenge Level:1
Nineteen is the smallest possible number of pairs of students who must be awarded the same mark.

This occurs when every possible mark from $0$ to $100$ is awarded to at least one student. This accounts for $101$ students and therefore the remaining $19$ students must all be awarded the same mark as exactly one of their colleagues.

The $120$ students are made up of $19$ pairs of students who are awarded the same mark and $82$ students who are all awarded a different mark from everyone else.

This problem is taken from the UKMT Mathematical Challenges.
View the archive of all weekly problems grouped by curriculum topic

View the previous week's solution
View the current weekly problem