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?

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!

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

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

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?

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

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?

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

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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 complete this jigsaw of the multiplication square?

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

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?

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....?

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

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

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

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?

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?

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

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

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

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

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

Use the interactivities to complete these Venn diagrams.

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How 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?

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

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.

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

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

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. . . .

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?

An environment which simulates working with Cuisenaire rods.

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?

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?

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

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?

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

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

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?

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

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