Work out how to light up the single light. What's the rule?

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

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?

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

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.

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

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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?

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?

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....?

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

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

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

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Can you complete this jigsaw of the multiplication square?

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

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

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

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

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

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

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

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!

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

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

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

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

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

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?

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?

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

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?

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

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

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?

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

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?

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

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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

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