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 primary teachers suggests ways in which to help children become better at working systematically.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
This challenge extends the Plants investigation so now four or more children are involved.
Use the clues to colour each square.
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. . . .
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
How many different triangles can you make on a circular pegboard that has nine pegs?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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 tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
A Sudoku with clues given as sums of entries.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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?
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 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.
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?
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....?
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 triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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?
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 work out how to balance this equaliser? You can put more
than one weight on a hook.
Find out what a "fault-free" rectangle is and try to make some of
What happens when you try and fit the triomino pieces into these
How many trains can you make which are the same length as Matt's, using rods that are identical?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Can you cover the camel with these pieces?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
How many different rhythms can you make by putting two drums on the
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.
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Can you find all the different ways of lining up these Cuisenaire
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back