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?

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

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.

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....?

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?

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

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

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?

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

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?

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

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

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

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?

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

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 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?

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

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

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

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

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!

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

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 chairs?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you complete this jigsaw of the multiplication square?

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

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 outline of Granma T?

Use the blue spot to help you move the yellow spot from one star to the other. How are the trails of the blue and yellow spots related?

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!

Use the interactivity or play this dice game yourself. How could you make it fair?

Can you fit the tangram pieces into the outline of the child walking home from school?

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

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 outline of this telephone?

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.

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

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

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

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?

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