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?
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 challenge extends the Plants investigation so now four or more children are involved.
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. . . .
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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 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?
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 challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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.
A challenging activity focusing on finding all possible ways of stacking rods.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
What could the half time scores have been in these Olympic hockey
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?
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.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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?
A Sudoku with clues given as sums of entries.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you use the information to find out which cards I have used?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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 clues to colour each square.
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
How many different triangles can you make on a circular pegboard
that has nine pegs?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Can you find all the different triangles on these peg boards, and
find their angles?
In this matching game, you have to decide how long different events take.
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?
Try this matching game which will help you recognise different ways of saying the same time interval.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?