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

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?

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

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

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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?

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

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?

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?

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

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?

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

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?

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

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?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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.

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

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. . . .

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!

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?

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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!

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.

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?

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

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

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?

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?

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?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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 the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

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

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?

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?

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.

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

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

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.

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

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

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

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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?

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