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 about Magic Squares in this article written for students. Why are they magic?!
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
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.
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 in them?
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.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
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?
Find out what a "fault-free" rectangle is and try to make some of
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.
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?
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.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
An investigation that gives you the opportunity to make and justify
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
How many trains can you make which are the same length as Matt's, using rods that are identical?
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 challenge extends the Plants investigation so now four or more children are involved.
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.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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 triangles can you make on a circular pegboard that has nine pegs?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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 information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
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?
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?
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.
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you find all the different triangles on these peg boards, and
find their angles?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Can you cover the camel with these pieces?