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?

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

An environment which simulates working with Cuisenaire rods.

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?

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

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?

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?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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.

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

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

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

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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?

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

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

How many different rhythms can you make by putting two drums on the wheel?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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

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

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

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

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Can you complete this jigsaw of the multiplication square?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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

Can you hang weights in the right place to make the equaliser balance?

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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

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

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?

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

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

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

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

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