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?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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

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

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....?

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?

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

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

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

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

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

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

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

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

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

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

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

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

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?

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

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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

Move just three of the circles so that the triangle faces in the opposite direction.

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

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

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

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.

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?

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?

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?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Sort the houses in my street into different groups. Can you do it in any other ways?

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

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

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

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

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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?

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

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

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

A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.

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

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

Use the interactivity or play this dice game yourself. How could you make it fair?