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.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
This Sudoku combines all four arithmetic operations.
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
Two sudokus in one. Challenge yourself to make the necessary
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
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. . . .
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.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Four small numbers give the clue to the contents of the four
You need to find the values of the stars before you can apply normal Sudoku rules.
A Sudoku with clues as ratios.
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.
A Sudoku with clues given as sums of entries.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
This Sudoku requires you to do some working backwards before working forwards.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
Use the differences to find the solution to this Sudoku.
A Sudoku with a twist.
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?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
The clues for this Sudoku are the product of the numbers in adjacent squares.
A Sudoku with clues as ratios or fractions.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
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.
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.
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
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?
A few extra challenges set by some young NRICH members.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
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.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?