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.
Solve the equations to identify the clue numbers in this Sudoku 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
A Sudoku with a twist.
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.
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?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
The challenge is to find the values of the variables if you are to
solve this Sudoku.
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.
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.
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?
Four small numbers give the clue to the contents of the four
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
An introduction to bond angle geometry.
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!
You have twelve weights, one of which is different from the rest.
Using just 3 weighings, can you identify which weight is the odd
one out, and whether it is heavier or lighter than the rest?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
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.
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A pair of Sudoku puzzles that together lead to a complete solution.
You need to find the values of the stars before you can apply normal Sudoku rules.
A Sudoku with clues as ratios.
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?
A Sudoku that uses transformations as supporting clues.
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.
Use the differences to find the solution to this Sudoku.
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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.
Use the clues about the shaded areas to help solve this sudoku
Two sudokus in one. Challenge yourself to make the necessary
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?
A Sudoku with clues as ratios or fractions.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.