This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
A Sudoku with clues given as sums of entries.
Find out about Magic Squares in this article written for students. Why are they magic?!
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
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.
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Find out what a "fault-free" rectangle is and try to make some of
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?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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....?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
How many models can you find which obey these rules?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
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 put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Find all the numbers that can be made by adding the dots on two dice.
Can you find all the different ways of lining up these Cuisenaire
How many different triangles can you make on a circular pegboard that has nine pegs?