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

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

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

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

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

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

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?

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.

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

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!

An interactive activity for one to experiment with a tricky tessellation

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

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

Can you complete this jigsaw of the multiplication square?

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.

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?

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

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?

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

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....?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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

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

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

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?

Train game for an adult and child. Who will be the first to make the train?

You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?

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

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

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?

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?

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

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

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

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

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

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?

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

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