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

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!

Use the information about Sally and her brother to find out how many children there are in the Brown family.

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

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?

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

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

How many trains can you make which are the same length as Matt's, using rods that are identical?

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

How many right angles can you make using two sticks?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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

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?

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?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

How many different rhythms can you make by putting two drums on the wheel?

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

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

Make one big triangle so the numbers that touch on the small triangles add to 10.

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?

Use the interactivity to sort these numbers into sets. Can you give each set a name?

What happens when you try and fit the triomino pieces into these two grids?

Can you hang weights in the right place to make the equaliser balance?

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

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

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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

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?

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

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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.

Can you fit the tangram pieces into the outline of Granma T?

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?

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

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

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

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?