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?

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

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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

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?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Sort the houses in my street into different groups. Can you do it in any other ways?

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

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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

How many trains can you make which are the same length as Matt's, using rods that are identical?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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

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

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

What happens when you try and fit the triomino pieces into these two grids?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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?

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?

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....?

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

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

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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?

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?

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

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

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

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?

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

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

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

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

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

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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

Exchange the positions of the two sets of counters in the least possible number of moves

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?

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.

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.

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?