The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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 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?
A Sudoku with clues given as sums of entries.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Find out what a "fault-free" rectangle is and try to make some of
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
Use the clues about the symmetrical properties of these letters to
place them on the grid.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
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.
How many models can you find which obey these rules?
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?
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.
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
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. . . .
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
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....?
Find out about Magic Squares in this article written for students. Why are they magic?!
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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 solutions can you find to this sum? Each of the different letters stands for a different number.
Use the clues to colour each square.
How many different triangles can you make on a circular pegboard
that has nine pegs?
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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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?
How many trains can you make which are the same length as Matt's,
using rods that are identical?
In this matching game, you have to decide how long different events take.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
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?
Can you find all the different triangles on these peg boards, and
find their angles?
Try this matching game which will help you recognise different ways of saying the same time interval.
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them