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.

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

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

Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

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

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

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?

Can you go from A to Z right through the alphabet in the hexagonal maze?

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

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?

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?

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

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

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?

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

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?

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

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.

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.

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

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

Use the information to work out how many gifts there are in each pile.

Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?

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?

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

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?

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?

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?

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?

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

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

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?

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?

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

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

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

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.

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

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

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

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?

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.

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?

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