Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?
How many noughts are at the end of these giant numbers?
In the diagram on the right, how many squares, of any size, are there whose entries add up to an even total?
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