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 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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

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

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

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

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!

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

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

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

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.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

How many different triangles can you make on a circular pegboard that has nine pegs?

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

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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.

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

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.

An interactive activity for one to experiment with a tricky tessellation

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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.

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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 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?

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

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. . . .

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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

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

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

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

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.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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

Try out the lottery that is played in a far-away land. What is the chance of winning?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.