In this article, the NRICH team describe the process of selecting solutions for publication on the site.
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 article for primary teachers suggests ways in which to help children become better at working systematically.
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 NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
A Sudoku with a twist.
Solve the equations to identify the clue numbers in this Sudoku problem.
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 clues given as sums of entries.
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.
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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 that uses transformations as supporting clues.
A Sudoku with clues as ratios.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
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.
Two sudokus in one. Challenge yourself to make the necessary
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
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.
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
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?
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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.
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. . . .
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?
Four small numbers give the clue to the contents of the four
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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?
A Sudoku with clues as ratios or fractions.
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
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?