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

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

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?

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

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?

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

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

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.

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.

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

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

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?

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?

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 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.

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

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

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?

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

Can you beat the computer in the challenging strategy 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?

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

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?

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.

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

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?

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?

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?

Three teams have each played two matches. The table gives the total number points and goals scored for and against each team. Fill in the table and find the scores in the three matches.

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?

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

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

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

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 number the vertices, edges and faces of a tetrahedron so that the number on each edge is the mean of the numbers on the adjacent vertices and the mean of the numbers on the adjacent faces?

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.

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.

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.

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.

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

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?

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