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

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?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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

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

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

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

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?

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

In how many ways can you stack these rods, following the rules?

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

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

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?

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

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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

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

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

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

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.

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?

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

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?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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?

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

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

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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.

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

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

In this matching game, you have to decide how long different events take.

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

I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?

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?

Can you find the chosen number from the grid using the clues?

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.

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