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

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

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?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Find the frequency distribution for ordinary English, and use it to help you crack the code.

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

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

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

A game in which players take it in turns to choose a number. Can you block your opponent?

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

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

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

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

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

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

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

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

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.

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

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.

Can you find triangles on a 9-point circle? Can you work out their angles?

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.

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. . . .

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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

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. . . .

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.

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.

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

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.

Use Excel to explore multiplication of fractions.

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

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. . . .

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?

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?

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.

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