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?

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

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

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?

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?

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

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?

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....?

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

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

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

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

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?

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?

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

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

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

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

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

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?

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

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

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?

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

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 make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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

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

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Can you find all the different triangles on these peg boards, and find their angles?

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

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?

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?

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!

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

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

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

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

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

An interactive activity for one to experiment with a tricky tessellation

Can you use the interactive to complete the tangrams in the shape of butterflies?

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

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