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?
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.
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
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.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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.
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.
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 triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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?
Find out what a "fault-free" rectangle is and try to make some of
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
Investigate all the different squares you can make on this 5 by 5
grid by making your starting side go from the bottom left hand
point. Can you find out the areas of all these squares?
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?
What could the half time scores have been in these Olympic hockey matches?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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 ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
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. . . .
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
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.
Use the clues to colour each square.
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 solutions can you find to this sum? Each of the different letters stands for a different number.
Can you find all the different ways of lining up these Cuisenaire
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?
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 triangle.
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?
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.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
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?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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?