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?

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

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

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

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

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

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

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

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?

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?

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

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

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....?

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

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?

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

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?

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

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

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

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

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?

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

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?

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?

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

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

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

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

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

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

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

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?

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

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?

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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?

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

Stop the Clock game for an adult and child. How can you make sure you always win this game?

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

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

Can you fit the tangram pieces into the outline of this plaque design?

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.