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 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. . . .

An interactive activity for one to experiment with a tricky tessellation

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

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

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.

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

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

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?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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?

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?

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?

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

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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

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

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?

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?

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

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

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

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

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

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?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

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?

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

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

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

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

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?

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

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

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