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

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

Move just three of the circles so that the triangle faces in the opposite direction.

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

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

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

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?

Twenty four games for 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!

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

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

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.

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

Can you hang weights in the right place to make the equaliser balance?

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

Complete the squares - but be warned some are trickier than they look!

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

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

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?

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?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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

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....?

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

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

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

How many right angles can you make using two sticks?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

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.

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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?

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

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