My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

The practical nature of this paper-folding challenge made the solution tricky to explain but we received several very clear explanations.

In this article for teachers, Bernard describes ways to challenge higher-attaining children at primary level.

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?