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.

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

A tool for generating random integers.

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?

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

An environment that enables you to investigate tessellations of regular polygons

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. . . .

The classic vector racing game brought to a screen near you.

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

A metal puzzle which led to some mathematical questions.

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

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

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

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 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.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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?

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

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....?

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

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

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

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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 fit the tangram pieces into the outlines of these clocks?

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.

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 fit the tangram pieces into the outlines of the chairs?

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

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

How many different rhythms can you make by putting two drums on the wheel?

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

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?

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.

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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