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.
A Sudoku with clues given as sums of entries.
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
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?
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?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
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?
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.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Investigate all the different squares you can make on this 5 by 5
grid by making your starting side go from the bottom left hand
point. Can you find out the areas of all these squares?
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 solutions can you find to this sum? Each of the different letters stands for a different number.
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Use the clues about the symmetrical properties of these letters to
place them on the grid.
What is the greatest number of counters you can place on the grid
below without four of them lying at the corners of a square?
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.
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?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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.
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
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many trains can you make which are the same length as Matt's,
using rods that are identical?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Here are four cubes joined together. How many other arrangements of
four cubes can you find? Can you draw them on dotty paper?
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. . . .
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.
Can you find all the different triangles on these peg boards, and
find their angles?
Can you find all the different ways of lining up these Cuisenaire
How many necklaces can you make that fit the rule? How do you know you've got them all?
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
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 different rhythms can you make by putting two drums on the
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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.
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?