Could games evolve by natural selection? Take part in this web experiment to find out!

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

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 beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.

Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in. . . .

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

To avoid losing think of another very well known game where the patterns of play are similar.

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

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.

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

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.

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

Use Excel to explore multiplication of fractions.

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?

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

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

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

Here is a chance to play a version of the classic Countdown Game.

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

A collection of our favourite pictorial problems, one for each day of Advent.

A tool for generating random integers.

Can you explain the strategy for winning this game with any target?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Work out how to light up the single light. What's the rule?

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

Match the cards of the same value.

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.