How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?

How many different shapes can you make by putting four right- angled isosceles triangles together?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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

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

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?

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

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

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

One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

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?

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?

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?

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?

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?

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

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.

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

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?

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?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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

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

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

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

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?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

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

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

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

Four children were sharing a set of twenty-four butterfly cards. Are there any cards they all want? Are there any that none of them want?

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?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

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?

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.

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?

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?