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

Work out how to light up the single light. What's the rule?

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

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do 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?

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.

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

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

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?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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

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?

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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

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!

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

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!

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

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

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?

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

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?

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

Can you complete this jigsaw of the multiplication square?

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

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?

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

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.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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

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. . . .

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

An interactive activity for one to experiment with a tricky tessellation

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

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

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?

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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

Can you work out what is wrong with the cogs on a UK 2 pound coin?

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

Can you fit the tangram pieces into the outlines of these clocks?