Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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.
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.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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 pair of Sudoku puzzles that together lead to a complete solution.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Use the differences to find the solution to this Sudoku.
Four small numbers give the clue to the contents of the four
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?
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?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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 as ratios or fractions.
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
A Sudoku with clues as ratios.
A Sudoku that uses transformations as supporting clues.
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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.
You need to find the values of the stars before you can apply normal Sudoku rules.
Use the clues about the shaded areas to help solve this sudoku
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Two sudokus in one. Challenge yourself to make the necessary
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
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?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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.
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. . . .
Find out about Magic Squares in this article written for students. Why are they magic?!
A Sudoku with a twist.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
This Sudoku combines all four arithmetic operations.
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.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Find all the ways of placing the numbers 1 to 9 on a W shape, with
3 numbers on each leg, so that each set of 3 numbers has the same
The challenge is to find the values of the variables if you are to
solve this Sudoku.
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?