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

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

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

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....?

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?

An environment which simulates working with Cuisenaire rods.

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!

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

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

Sort the houses in my street into different groups. Can you do it in any other ways?

Use the interactivities to complete these Venn diagrams.

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

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

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

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

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

Can you complete this jigsaw of the multiplication square?

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

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

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

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

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

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

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

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

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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

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

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?

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

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?

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?

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?

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?

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

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

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

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

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

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?

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

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