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

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?

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

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?

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?

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

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

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?

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

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?

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?

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

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?

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

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

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

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

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?

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?

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

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?

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?

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.

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?

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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?

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

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?

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

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?

Semaphore is a way to signal the alphabet using two flags. You might want to send a message that contains more than just letters. How many other symbols could you send using this code?

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

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

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

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?

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.

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?

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

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

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

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

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

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?

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.

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?