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?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

If you have only four weights, where could you place them in order to balance this equaliser?

Here is a chance to play a version of the classic Countdown Game.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

An environment which simulates working with Cuisenaire rods.

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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 complete this jigsaw of the multiplication square?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Find out what a "fault-free" rectangle is and try to make some of your own.

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

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?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

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

Can you find all the different ways of lining up these Cuisenaire rods?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?