In this article, the NRICH team describe the process of selecting solutions for publication on the site.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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.
This Sudoku requires you to do some working backwards before working forwards.
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 Sudoku with clues as ratios or fractions.
Given the products of diagonally opposite cells - can you complete this Sudoku?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
A Sudoku with clues given as sums of entries.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
A Sudoku that uses transformations as supporting clues.
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 as ratios.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Solve the equations to identify the clue numbers in this Sudoku problem.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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.
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
A Sudoku with a twist.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
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.
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.
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.
Two sudokus in one. Challenge yourself to make the necessary
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?
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?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
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?
You need to find the values of the stars before you can apply normal Sudoku rules.
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
Four small numbers give the clue to the contents of the four
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. . . .
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?
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 pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
A few extra challenges set by some young NRICH members.