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

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. . . .

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.

This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!

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?

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.

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

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

Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing

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.

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

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 counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

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

This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

With red and blue beads on a circular wire; 'put a red bead between any two of the same colour and a blue between different colours then remove the original beads'. Keep repeating this. What happens?

Use Excel to explore multiplication of fractions.

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

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. . . .

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

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

Can you work through these direct proofs, using our interactive proof sorters?

A tool for generating random integers.

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

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?

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.

Can you beat the computer in the challenging strategy game?

Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.

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

This is an interactivity in which you have to sort into the correct order the steps in the proof of the formula for the sum of a geometric series.

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.

Match pairs of cards so that they have equivalent ratios.

Use Excel to investigate the effect of translations around a number grid.

Use an interactive Excel spreadsheet to investigate factors and multiples.

Use Excel to practise adding and subtracting fractions.

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

Use an interactive Excel spreadsheet to explore number in this exciting game!