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.
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?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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?
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?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
A pair of Sudoku puzzles that together lead to a complete solution.
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.
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. . . .
A Sudoku with clues as ratios.
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.
A Sudoku with a twist.
Special clue numbers related to the difference between numbers in
two adjacent cells and values of the stars in the "constellation"
make this a doubly interesting problem.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Two sudokus in one. Challenge yourself to make the necessary
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
A Sudoku with clues as ratios or fractions.
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.
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
A Sudoku that uses transformations as supporting clues.
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.
Use the differences to find the solution to this Sudoku.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
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.
A Sudoku based on clues that give the differences between adjacent cells.
This Sudoku requires you to do some working backwards before working forwards.
Solve the equations to identify the clue numbers in this Sudoku problem.
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.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Use the clues about the shaded areas to help solve this sudoku
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.
Label this plum tree graph to make it totally magic!
A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?
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?
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
A Sudoku with clues given as sums of entries.
The challenge is to find the values of the variables if you are to
solve this Sudoku.