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 shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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?

What is the best way to shunt these carriages so that each train can continue its journey?

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

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

Make a cube out of straws and have a go at this practical challenge.

Can you fit the tangram pieces into the outline of this junk?

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Can you fit the tangram pieces into the outline of Mai Ling?

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

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

Can you fit the tangram pieces into the outline of this telephone?

Can you work out what is wrong with the cogs on a UK 2 pound coin?

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

What is the greatest number of squares you can make by overlapping three squares?

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

Can you make a 3x3 cube with these shapes made from small cubes?

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?

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Think of a number, square it and subtract your starting number. Is the number youâ€™re left with odd or even? How do the images help to explain this?

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

Exploring and predicting folding, cutting and punching holes and making spirals.

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 cube that is green all over AND a 2 x 2 cube that is yellow all over?

Exchange the positions of the two sets of counters in the least possible number of moves

Can you fit the tangram pieces into the outlines of the chairs?

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

Can you cut up a square in the way shown and make the pieces into a triangle?

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

Can you fit the tangram pieces into the outline of Little Ming?

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

Can you fit the tangram pieces into the outlines of these people?

Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?

Can you fit the tangram pieces into the outline of this goat and giraffe?