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!

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

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

Can you explain the strategy for winning this game with any target?

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

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

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?

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

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?

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

An interactive activity for one to experiment with a tricky tessellation

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?

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

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

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

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?

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

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.

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

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

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

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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?

Use the interactivities to complete these Venn diagrams.

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?

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?

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?

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?

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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

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. . . .

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

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?

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

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?

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

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

Work out the fractions to match the cards with the same amount of money.

Can you complete this jigsaw of the multiplication square?

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....?

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.

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

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

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

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