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 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
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.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
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.
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.
If you have only four weights, where could you place them in order to balance this equaliser?
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?
Try out the lottery that is played in a far-away land. What is the chance of winning?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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....?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
Choose a symbol to put into the number sentence.
How many different triangles can you make on a circular pegboard that has nine pegs?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
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?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
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?
Can you complete this jigsaw of the multiplication square?
Can you find all the different triangles on these peg boards, and find their angles?
Can you explain the strategy for winning this game with any target?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
A card pairing game involving knowledge of simple ratio.
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!
A train building game for 2 players.
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. . . .
A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
An interactive activity for one to experiment with a tricky tessellation