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?

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

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?

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

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?

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

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

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?

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?

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?

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

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.

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

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.

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

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

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.

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

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

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?

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?

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.

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

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?

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?

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?

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.

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

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

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.

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

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

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

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

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?

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

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?

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

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

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?

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.

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?

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?

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

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).