Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, 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?
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.
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?
When I park my car in Mathstown, there are two car parks to choose from. Which car park should I use?
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
The twelve edge totals of a standard six-sided die are distributed symmetrically. Will the same symmetry emerge with a dodecahedral die?
Give your further pure mathematics skills a workout with this interactive and reusable set of activities.