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

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

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

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?

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

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

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

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?

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

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?

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

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

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

Find out what a "fault-free" rectangle is and try to make some of your own.

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

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

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?

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....?

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

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

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

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?

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

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?

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?

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?

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

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

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?

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?

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

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

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

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

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!

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?

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

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

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?

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?

Stop the Clock game for an adult and child. How can you make sure you always win this game?

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

Can you find all the different triangles on these peg boards, and find their angles?

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.