This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
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 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?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Try out the lottery that is played in a far-away land. What is the chance of winning?
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 find all the different ways of lining up these Cuisenaire rods?
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?
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?
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?
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....?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Choose a symbol to put into the number sentence.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
Can you find all the different triangles on these peg boards, and find their angles?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
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.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Find out what a "fault-free" rectangle is and try to make some of your own.
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?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
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 make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?
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 the child walking home from school?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
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.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you fit the tangram pieces into the outline of Little Fung at the table?
A card pairing game involving knowledge of simple ratio.
A train building game for 2 players.
If you have only four weights, where could you place them in order to balance this equaliser?
Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?