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....?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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 trains can you make which are the same length as Matt's, using rods that are identical?
What happens when you try and fit the triomino pieces into these
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Can you find all the different ways of lining up these Cuisenaire
An environment which simulates working with Cuisenaire rods.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white 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 cover the camel with these pieces?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
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 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?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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!
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Can you complete this jigsaw of the multiplication square?
How many different rhythms can you make by putting two drums on the
An odd version of tic tac toe
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Here is a chance to play a version of the classic Countdown Game.
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?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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?
Use the clues to colour each square.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
A variant on the game Alquerque
Move just three of the circles so that the triangle faces in the
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
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 activity for one to experiment with a tricky tessellation
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.