Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
Can you go from A to Z right through the alphabet in the hexagonal maze?
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.
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.
If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
Can you find a path from a number at the top of this network to the bottom which goes through each number from 1 to 9 once and once only?
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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Use these four dominoes to make a square that has the same number of dots on each side.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
There were 22 legs creeping across the web. How many flies? How many spiders?
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Can you use the information to find out which cards I have used?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?
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?
You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
56 406 is the product of two consecutive numbers. What are these two numbers?
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Using only six straight cuts, find a way to make as many pieces of pizza as possible. (The pieces can be different sizes and shapes).
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?