In this article, the NRICH team describe the process of selecting solutions for publication on the site.
This article for primary teachers suggests ways in which to help children become better at working systematically.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Use the clues to colour each square.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you cover the camel with these pieces?
Can you find all the different triangles on these peg boards, and
find their angles?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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 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 your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
Ben has five coins in his pocket. How much money might he have?
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?
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?
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
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?
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?
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
Can you find all the different ways of lining up these Cuisenaire
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
How many different rhythms can you make by putting two drums on the
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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.
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. . . .
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....?
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 different triangles can you draw on the dotty grid which each have one dot in the middle?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
A challenging activity focusing on finding all possible ways of stacking rods.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
What happens when you try and fit the triomino pieces into these
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.