Here are some rods that are different colours. How could I make a yellow rod using white and red rods?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
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?
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?
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?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
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?
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?
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?
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.
Explore the different snakes that can be made using 5 cubes.
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
My coat has three buttons. How many ways can you find to do up all the buttons?
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?
The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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?
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?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
An environment which simulates working with Cuisenaire rods.
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.
Use these head, body and leg pieces to make Robot Monsters which are different heights.
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?
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?
Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
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?
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?
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.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
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?
Can you fill in the empty boxes in the grid with the right shape and colour?
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 put five cereal packets together to make different shapes if you must put them face-to-face?