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?

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

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

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?

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?

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

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....?

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

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?

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!

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

An environment which simulates working with Cuisenaire rods.

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

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?

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

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?

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

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?

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

Can you complete this jigsaw of the multiplication square?

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

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

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

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?

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?

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

An interactive activity for one to experiment with a tricky tessellation

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?

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

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

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

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

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

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?

Train game for an adult and child. Who will be the first to make the train?

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

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?

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

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

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.

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .