In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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

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

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

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

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

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

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?

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....?

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

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

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

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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

Can you draw a square in which the perimeter is numerically equal to the area?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

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

These practical challenges are all about making a 'tray' and covering it with paper.

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

Investigate the different ways you could split up these rooms so that you have double the number.

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

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?

An activity making various patterns with 2 x 1 rectangular tiles.

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

Find your way through the grid starting at 2 and following these operations. What number do you end on?