The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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.
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.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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.
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?
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 find six numbers to go in the Daisy from which you can make
all the numbers from 1 to a number bigger than 25?
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Use the clues to colour each square.
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....?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
How many trains can you make which are the same length as Matt's,
using rods that are identical?
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
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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. . . .
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
Can you find all the different triangles on these peg boards, and
find their angles?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
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 triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
A Sudoku with clues given as sums of entries.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
This train line has two tracks which cross at different points. Can
you find all the routes that end at Cheston?
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?
This article for primary teachers suggests ways in which to help children become better at working systematically.
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?
Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them