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

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?

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

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

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?

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?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

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?

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

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

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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?

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

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 ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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.

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.

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

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

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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?

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

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

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?

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

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

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?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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

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?

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

Find out what a "fault-free" rectangle is and try to make some of your own.

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?

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?

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

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

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?

An activity making various patterns with 2 x 1 rectangular tiles.

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

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

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Number problems at primary level that require careful consideration.

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?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.