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.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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.
A Sudoku with clues given as sums of entries.
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.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
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?
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?
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?
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?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Use the clues to colour each square.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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....?
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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.
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.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.
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?
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?
Can you find all the different ways of lining up these Cuisenaire
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
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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. . . .
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Find out about Magic Squares in this article written for students. Why are they magic?!
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
How many different rhythms can you make by putting two drums on the
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
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back