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

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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?

If you have only four weights, where could you place them in order to balance this equaliser?

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

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

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

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

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?

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?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

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!

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?

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?

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

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?

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....?

Can you find all the different ways of lining up these Cuisenaire rods?

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

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

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

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

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

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

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

Can you fit the tangram pieces into the outlines of these clocks?

An environment which simulates working with Cuisenaire rods.

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 outlines of the candle and sundial?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

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

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

Can you logically construct these silhouettes using the tangram pieces?

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

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?

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

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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 Granma T?

Can you fit the tangram pieces into the outlines of these people?

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?