Can you fill in the empty boxes in the grid with the right shape and colour?

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.

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

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?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

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

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

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

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

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.

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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?

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

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

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?

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?

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

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

How many ways can you find of tiling the square patio, using square tiles of different sizes?

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

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

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

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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

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?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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?

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?