Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
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?
Use the clues to colour each square.
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white 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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
How many different rhythms can you make by putting two drums on the wheel?
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?
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?
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
How many trains can you make which are the same length as Matt's, using rods that are identical?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
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 information about Sally and her brother to find out how many children there are in the Brown family.
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
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?
Choose a symbol to put into the number sentence.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
Investigate the different sounds you can make by putting the owls and donkeys on the wheel.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
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?
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?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Train game for an adult and child. Who will be the first to make the train?