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.

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.

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. . . .

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.

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?

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

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

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

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

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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 beat the computer in the challenging strategy game?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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.

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

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

Can you fit the tangram pieces into the outlines of the candle and sundial?

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

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

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

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

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

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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

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

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?

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.

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

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

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

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

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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.

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

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

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 fit the tangram pieces into the outlines of these clocks?

Can you fit the tangram pieces into the outline of Little Fung at the table?

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

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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.