Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
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?
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?
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?
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 find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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....?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
An environment which simulates working with Cuisenaire rods.
If you have only four weights, where could you place them in order to balance this equaliser?
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?
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!
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?
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?
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.
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
How many different triangles can you make on a circular pegboard that has nine pegs?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you find all the different triangles on these peg boards, and find their angles?
Here is a chance to play a version of the classic Countdown Game.
Can you complete this jigsaw of the multiplication square?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
A card pairing game involving knowledge of simple ratio.
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.
An interactive activity for one to experiment with a tricky tessellation
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
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?
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?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Choose a symbol to put into the number sentence.
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?
A generic circular pegboard resource.