If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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.

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

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

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?

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!

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?

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

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?

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!

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

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.

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

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?

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 number has 903 digits. What is the sum of all 903 digits?

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

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

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

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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?

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

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

Got It game for an adult and child. How can you play so that you know you will always win?

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

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

This dice train has been made using specific rules. How many different trains can you make?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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?

Can you score 100 by throwing rings on this board? Is there more than way to do it?

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?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

Are these statements always true, sometimes true or never true?

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

This challenge combines addition, multiplication, perseverance and even proof.

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

This task combines spatial awareness with addition and multiplication.

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?