The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
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.
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.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
Find out what a "fault-free" rectangle is and try to make some of
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
A Sudoku with clues given as sums of entries.
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Use the clues to colour each square.
How many trains can you make which are the same length as Matt's,
using rods that are identical?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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....?
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?
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?
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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
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 journeys could you make if you were going to
visit four stations in this network? How about if there were five
stations? Can you predict the number of journeys for seven
In this matching game, you have to decide how long different events take.
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
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
Can you find all the different ways of lining up these Cuisenaire
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
This challenge is about finding the difference between numbers which have the same tens digit.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.