In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Can you replace the letters with numbers? Is there only one solution in each case?

How many trapeziums, of various sizes, are hidden in this picture?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Can you use this information to work out Charlie's house number?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

There are lots of different methods to find out what the shapes are worth - how many can you find?

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

Investigate the different ways you could split up these rooms so that you have double the number.

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?