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 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?

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

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?

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.

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?

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

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.

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?

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?

Sam sets up displays of cat food in his shop in triangular stacks. If Felix buys some, then how can Sam arrange the remaining cans in triangular stacks?

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?

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

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?

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

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.

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?

A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?

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

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

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

How many different rhythms can you make by putting two drums on the wheel?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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?

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

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?

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?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

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?

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

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

If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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?

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

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

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?

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

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?

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?

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.

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

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

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

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?

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