In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

This challenge is about finding the difference between numbers which have the same tens digit.

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

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?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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!

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

What two-digit numbers can you make with these two dice? What can't you make?

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

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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!

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

This task follows on from Build it Up and takes the ideas into three dimensions!

Can you find all the ways to get 15 at the top of this triangle of numbers?

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.

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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.

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

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?

You have 5 darts and your target score is 44. How many different ways could you score 44?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Find all the numbers that can be made by adding the dots on two dice.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

My coat has three buttons. How many ways can you find to do up all the buttons?

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?