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.
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?
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?
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?
Use the differences to find the solution to this Sudoku.
A pair of Sudoku puzzles that together lead to a complete solution.
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?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Four small numbers give the clue to the contents of the four
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
This Sudoku, based on differences. Using the one clue number can you find the solution?
An introduction to bond angle geometry.
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.
Find all the ways of placing the numbers 1 to 9 on a W shape, with
3 numbers on each leg, so that each set of 3 numbers has the same
Take three whole numbers. The differences between them give you
three new numbers. Find the differences between the new numbers and
keep repeating this. What happens?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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 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.
You need to find the values of the stars before you can apply normal Sudoku rules.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
This Sudoku combines all four arithmetic operations.
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.
A Sudoku with clues as ratios.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
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 Sudoku that uses transformations as supporting clues.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Can you coach your rowing eight to win?
Use the clues about the shaded areas to help solve this sudoku
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. . . .
Find out about Magic Squares in this article written for students. Why are they magic?!
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Two sudokus in one. Challenge yourself to make the necessary
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 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 numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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?
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.
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?