An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

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

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.

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

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.

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. . . .

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.

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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.

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.

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 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.

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. . . .

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.

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

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

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.

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

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

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

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

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

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

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?

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.

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

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?

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?

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?

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?

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

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

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

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...

Work out the fractions to match the cards with the same amount of money.

Find out what a "fault-free" rectangle is and try to make some of your own.

What is the greatest number of squares you can make by overlapping three squares?

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.

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