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

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

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

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

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

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

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?

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?

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

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?

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?

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?

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

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....?

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

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

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?

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

The pages of my calendar have got mixed up. Can you sort them out?

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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.

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.

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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

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

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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

Using the statements, can you work out how many of each type of rabbit there are in these pens?