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. . . .

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Place the numbers 1 to 10 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 your way through the grid starting at 2 and following these operations. What number do you end on?

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!

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

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

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!

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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.

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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

If you have only four weights, where could you place them in order to balance this equaliser?

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 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?

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?

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?

In this game for two players, the aim is to make a row of four coins which total one dollar.

This challenge extends the Plants investigation so now four or more children are involved.

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

A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!

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

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 challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

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.

Fill in the numbers to make the sum of each row, column and diagonal equal to 15.

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, focuses on 'open squares'. What would the next five open squares look like?

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

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.

A game for 2 players. Practises subtraction or other maths operations knowledge.

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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?

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?

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

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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?