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

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?

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

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?

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

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?

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....?

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!

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

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?

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

Can you complete this jigsaw of the multiplication square?

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

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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

Try out the lottery that is played in a far-away land. What is the chance of winning?

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?

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

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

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

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?

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?

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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

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

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

How many different triangles can you make on a circular pegboard that has nine pegs?

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

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

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

Can you find all the different triangles on these peg boards, and find their angles?

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

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

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

Use the interactivities to complete these Venn diagrams.

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

These interactive dominoes can be dragged around the screen.

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

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?