Show there are exactly 12 magic labellings of the Magic W using the
numbers 1 to 9. Prove that for every labelling with a magic total T
there is a corresponding labelling with a magic total 30-T.
Label this plum tree graph to make it totally magic!
Solve the equations to identify the clue numbers in this Sudoku problem.
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.
The challenge is to find the values of the variables if you are to
solve this Sudoku.
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Two sudokus in one. Challenge yourself to make the necessary
A Sudoku with clues as ratios.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
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. . . .
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.
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?
A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.
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.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
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?
Use the clues about the shaded areas to help solve this sudoku
This Sudoku combines all four arithmetic operations.
This Sudoku problem consists of a pair of linked standard Suduko puzzles each with some starting digits
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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.
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?
A Sudoku based on clues that give the differences between adjacent cells.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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.
This Sudoku requires you to do some working backwards before working forwards.
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.