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?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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.
A Sudoku with clues given as sums of entries.
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.
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
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....?
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.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
What could the half time scores have been in these Olympic hockey matches?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
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 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. . . .
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Find out what a "fault-free" rectangle is and try to make some of
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.
Can you find all the different triangles on these peg boards, and
find their angles?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many trains can you make which are the same length as Matt's, using rods that are identical?
Can you find all the different ways of lining up these Cuisenaire
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.
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.