Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.

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

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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?

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.

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

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?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

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.

Use these four dominoes to make a square that has the same number of dots on each side.

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

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 your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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

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?

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.

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?

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

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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?

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?

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?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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?

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

There were 22 legs creeping across the web. How many flies? How many spiders?

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

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?

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?

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?

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?

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.

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.

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

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

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.

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?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

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).