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

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.

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?

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?

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

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.

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?

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

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

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?

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?

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?

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.

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?

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?

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

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?

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

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

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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?

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?

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

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

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

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

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

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

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

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 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.

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?

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.

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?

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?

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?

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.

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

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?

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?

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?

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

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.

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.

Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?

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?

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