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?

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.

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?

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

Place the numbers 1 to 6 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?

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

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.

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

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?

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?

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

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?

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 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?

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.

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?

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?

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?

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

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

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?

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?

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?

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

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

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

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?

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.

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.

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?

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.

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

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

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.

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

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.

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

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?

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

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?

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

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

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?

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?