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

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

Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column

If you had 36 cubes, what different cuboids could you make?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

Try this matching game which will help you recognise different ways of saying the same time interval.

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

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?

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

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?

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

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

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

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

In this matching game, you have to decide how long different events take.

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

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?

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

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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?

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

These two group activities use mathematical reasoning - one is numerical, one geometric.

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.

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 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?

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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?

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?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

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

In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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?

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?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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?

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 help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

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.

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

How many trains can you make which are the same length as Matt's, using rods that are identical?

Can you find all the different ways of lining up these Cuisenaire rods?

How many different triangles can you make on a circular pegboard that has nine pegs?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?