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.
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.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
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?
Four small numbers give the clue to the contents of the four
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?
Use the differences to find the solution to this Sudoku.
Can you coach your rowing eight to win?
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?
A pair of Sudoku puzzles that together lead to a complete solution.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
It is possible to identify a particular card out of a pack of 15
with the use of some mathematical reasoning. What is this reasoning
and can it be applied to other numbers of cards?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Use the clues about the shaded areas to help solve this sudoku
Two sudokus in one. Challenge yourself to make the necessary
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
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 that uses transformations as supporting clues.
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?
Given the products of diagonally opposite cells - can you complete this Sudoku?
A Sudoku with clues as ratios or fractions.
The clues for this Sudoku are the product of the numbers in adjacent squares.
A Sudoku with clues as ratios.
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
The puzzle can be solved with the help of small clue-numbers which
are either placed on the border lines between selected pairs of
neighbouring squares of the grid or placed after slash marks on. . . .
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
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
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. . . .
This Sudoku combines all four arithmetic operations.
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?