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.
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?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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?
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?
A pair of Sudoku puzzles that together lead to a complete solution.
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?
Use the differences to find the solution to this Sudoku.
Four small numbers give the clue to the contents of the four
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?
Can you coach your rowing eight to win?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
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.
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?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
A Sudoku that uses transformations as supporting clues.
A Sudoku with clues as ratios.
You need to find the values of the stars before you can apply normal Sudoku rules.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Use the clues about the shaded areas to help solve this sudoku
An introduction to bond angle geometry.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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 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.
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?
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.
Given the products of adjacent cells, can you complete this Sudoku?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
A Sudoku with a twist.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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. . . .
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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.
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.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Given the products of diagonally opposite cells - can you complete this Sudoku?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow