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.

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

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?

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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

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

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

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?

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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?

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

A game for 2 people. Take turns joining two dots, until your opponent is unable to move.

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

Can you mark 4 points on a flat surface so that there are only two different distances between them?

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

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

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

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.

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

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

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

Can you fit the tangram pieces into the outline of the telescope and microscope?

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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!

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

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

Can you fit the tangram pieces into the outline of the child walking home from school?

What is the minimum number of squares a 13 by 13 square can be dissected into?

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

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

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

Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?

Can you visualise what shape this piece of paper will make when it is folded?

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

Can you logically construct these silhouettes using the tangram pieces?

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