Can you number the vertices, edges and faces of a tetrahedron so that the number on each edge is the mean of the numbers on the adjacent vertices and the mean of the numbers on the adjacent faces?

A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.

Can you make a 3x3 cube with these shapes made from small cubes?

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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?

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

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?

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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.

Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

Can you use the information to find out which cards I have used?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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?

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?

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?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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.

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?

Three teams have each played two matches. The table gives the total number points and goals scored for and against each team. Fill in the table and find the scores in the three matches.

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

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?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

56 406 is the product of two consecutive numbers. What are these two numbers?

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.

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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).

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

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?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

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?