Search / Ask a Question:
Tue, 29 Sep 2020

Sudoku and Symmetry

Most sudoku puzzles that you see - although not all - contain symmetry.

Sepcifically, they tend to contain rotational symmetry such that if the puzzle is rotated 180 degrees it looks the same.

This is visually quite pleasing, and infact some publishers require that their sudokus display symmetry or else they do not count it as a valid sudoku: for instance Nikoli in Japan apparently stipulates a sudoku must have symmetry and 32 givens or less to count as a valid sudoku or else it is rejected.

There are however many other types of symmetry that could be introduced: for instance different degrees of rotational symmetry, reflectional symmetry, combinations of all, and these have interesting names for non-mathematicians such as "full dihedral symmetry" which would leave most people none the wiser as to what exactly that meant! There are various websites that list many types of sudoku symmetry with examples of each.

So does symmetry help with solving sudoku? The jury is out, with most people based on reading various sudoku blogs thinking symmetry is just for effect, and that if anything it might make puzzles easier, often by introducing a given (starting number) that is not required to solve but was required for the symmetry to hold.

As soon as you add one number to a sudoku puzzle with the most common form of symmetry then the symmetry is broken (well, unless you enter the middle digit in a 9x9 grid!).

However there are occasions on which symmetry can help out, and particularly if you have the same digit in two cells that share symmetry you may be able to repeat a logical rule you used on one to make progress with your solve on its partner cell.

If you are creating your own sudoku, then you should definitely spend the extra few minutes to introduce symmetry to your puzzles. Most people who play sudoku are used to seeing symmetrical grids too, just like with crosswords, and therefore something that is non-symmetric can strike the player as odd. Many publishers stipulate that they want symmetrical sudoku grids.

And of course the most common type of symmetry is trivial for a programmer to introduce to your sudoku puzzles.

If you are someone who hand writes sudoku puzzles, do you find creating a puzzle with symmetry any easier or harder than creating one without symmetry? Do you have any comments in general about sudoku and symmetry? If so please do post below in the comments section!
Date written: 01 Dec 2010

Category: sudoku | Keywords: symmetry


Puzzle Videos: Learn to Solve

How to solve Hanjie Puzzles
A fun logic puzzle, hanjies result in a simple piece of grid art being created. If you're new to this puzzle type but are intrigued and would like to give it a go, this video has a walkthrough of how to solve a simple hanjie puzzle to start you on your hanjie-solving adventures...



Hanjie is a fun puzzle, would you like to try the easy example in this video? You can do so here: Easy Online Hanjie Puzzle


Read about other Puzzles




Comment on this blog post

If you would like to comment on this post, please enter your comments below; all fields are mandatory. Posts are moderated before display.
Your name:


Your comments:


Human testing question:
Is our favourite word: obscurity, clarity or semi-transparent?



Back to World of Puzzles
Puzzle Solutions
i Newspaper Solutions

Book Ideas: For Children
brain training puzzles for kids
Brain Training for Kids

Book Ideas: For Adults
crosswords for adults
Crosswords for Adults

Key Links for Publishers

View a single page overview
list of puzzles
with a picture of each and a link to more information.

list of kids puzzles

Contact us


Word Puzzles
Buy Crosswords
Children's Puzzles
Wordsearch
CodeWords
Arrow words
Kriss Kross
Word Ladder
Word Wheel

Number & Colouring Puzzles
Buy Sudoku
Children's Sudoku
Samurai Sudoku
Jigsaw Sudoku
Futoshiki
Mind Games
Killer Sudoku
Kakuro
Chess Puzzles
A - Z of Puzzles
Colour By Number
Dot To Dot
Adult Colouring


Puzzle Tools
Puzzle FAQ
Codeword Solver
Rhyming Dictionary
Puzzle Solving Tools

Services
Puzzles for Apps
Article Writing
Themed Puzzle Pages
Press Ready Puzzles
Questions
Page Fillers

View all services
© Clarity Media Ltd., 2020, company number 5465221 | Contact Us | Privacy Policy