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.
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
You have been given nine weights, one of which is slightly heavier
than the rest. Can you work out which weight is heavier in just two
weighings of the balance?
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
Can you recreate these designs? What are the basic units? What
movement is required between each unit? Some elegant use of
procedures will help - variables not essential.
A Sudoku with clues as ratios or fractions.
Given the products of diagonally opposite cells - can you complete this Sudoku?
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
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 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 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.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
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.
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?
A few extra challenges set by some young NRICH members.
A Sudoku that uses transformations as supporting clues.
A Sudoku with clues as ratios.
A Sudoku with a twist.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Two sudokus in one. Challenge yourself to make the necessary
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. . . .
Four small numbers give the clue to the contents of the four
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
A Sudoku based on clues that give the differences between adjacent cells.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
A pair of Sudoku puzzles that together lead to a complete solution.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
A Sudoku with clues given as sums of entries.
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.
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Imagine a stack of numbered cards with one on top. Discard the top,
put the next card to the bottom and repeat continuously. Can you
predict the last card?