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?

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

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

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?

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?

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

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

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

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

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!

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?

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

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....?

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

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

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

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

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?

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

Can you explain the strategy for winning this game with any target?

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?

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?

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?

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

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

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?

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

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

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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

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.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight 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 fit the tangram pieces into the outline of Mai Ling?

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

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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

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

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

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?

Can you fit the tangram pieces into the outline of Granma T?

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

An environment which simulates working with Cuisenaire rods.

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?

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.