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 pair of Sudoku puzzles that together lead to a complete solution.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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. . . .
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.
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
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.
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.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Four small numbers give the clue to the contents of the four surrounding cells.
A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
You need to find the values of the stars before you can apply normal Sudoku rules.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
Given the products of diagonally opposite cells - can you complete this Sudoku?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
Use the differences to find the solution to this Sudoku.
A few extra challenges set by some young NRICH members.
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.
This Sudoku combines all four arithmetic operations.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
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 clues about the shaded areas to help solve this sudoku
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?
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.
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.
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.
Two sudokus in one. Challenge yourself to make the necessary connections.
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
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 total.
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Given the products of adjacent cells, can you complete this Sudoku?
This challenge extends the Plants investigation so now four or more children are involved.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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 Sudoku with clues as ratios.