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

Use the interactivities to complete these Venn diagrams.

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

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

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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!

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

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

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.

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?

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?

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

These interactive dominoes can be dragged around the screen.

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?

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?

An interactive activity for one to experiment with a tricky tessellation

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!

Can you complete this jigsaw of the multiplication square?

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

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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

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

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

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

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

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

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

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

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?

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!

What is the greatest number of squares you can make by overlapping three squares?

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

Can you fit the tangram pieces into the outline of this telephone?

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

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

Can you fit the tangram pieces into the outlines of the chairs?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

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 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?

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