## An Index of Sudoku Strategies

Sudoku is a game of pure logical deduction, just like Kakuro and other Japanese number puzzles. Unlike games of luck such as card and bingo games, guessing is never required.

I’ve now learned a number of methods for solving tough Sudoku puzzles by hand, including X-Wing, Swordfish, Jellyfish, Squirmbag, Turbot-fish, XY-Wing, XYZ-Wing, Conjugate Pairs, Bowman Bingo, Simple Coloring, Super Coloring and Tabling.

I have not yet found a single website that explains all of these techniques in one location, so I thought I’d provide some links to the various websites where I discovered these techniques.

The Sudoku Techniques page at SadMan Software explains most (but not all) of the simpler “pattern-matching” techniques. Techniques explained here include:

- Naked Single
- Hidden Single
- Block and Column/Row
- Block / Block
- Naked Subset
- Hidden Subset
- XWing & Swordfish
- XY-Wing
- Coloring / Colourring
- Forcing Chains
- Nishio

The first 6 methods listed on Sadman’s site (Naked Single thru Hidden Subset) are sufficient to solve all the “Easy” and “Intermediate” puzzles I provide on this site, and most easy/medium newspaper puzzles.

The Solving Sudoku Forum at setbb.com and to a lesser extent, the Solving Techniques Forum at sudoku.com had vigorous discussions in spring 2005 (when Sudoku was a raging fad in the UK) in which a few new techniques were discovered. Some of these discussion threads contain the original discoveries of methods listed at the above site, and some of these patterns have not yet been included there (although I find them very useful!). These discussions still continue today, but are more focused on more advanced techniques which are more appropriate for computers.

Interesting threads include:

- XY Wing
- XYZ-Wing
- Turbot Fish (a very common kind of forcing chain)
- Bowman Bingo (also related to Forcing Chains)
- Nishio
- Simple Colouring (described midway thru this thread)
- Ultracolouring
- Table Solving & Advanced Colouring

Although the XWing (and Swordfish) patterns are easy to spot, statistical analysis shows they do not occur very often. I’ve

found the XY-Wing, XYZ Wing and Turbot Fish patterns occur *much* more frequently, and are good weapons to have in your solving arsenal. These strategies are especially good for solving the super tough puzzles I offer here .

I find the various coloring/colouring and tabling methods to be too work-intensive for human use – they really make more sense for computer solvers, but sometimes they are the only methods you can use to solve a really hard puzzle.

Finally, Michael’s Mepham’s Book of Sudoku contains an excellent 10-page introduction with various solving strategies, in addition to numerous puzzles.

UPDATE: Eduyng CastaÃ±o wrote to me about a technique he has discovered called Golden Chains (pdf). The technique is a generalization of XY-Wing, and solves many of the same puzzles that can be solved by other advanced techniques such as conjugate pairs, nishio and coloring, but it does not feel as much like ‘guessing’ as those other techniques. I have successfully used it to solve a number of my ‘super tough’ puzzles. It is particularly effective when a puzzle has been reduced to a lot of squares containing only 2 possibilities.

December 1st, 2005 at 9:05 am

Great guide to Sudoku! Well done!

January 13th, 2006 at 12:23 pm

[...] The technique is a generalization of XY-Wing, and solves many (but not all) of the same puzzles that can be solved by other advanced techniques such as conjugate pairs, nishio and coloring. Unlike those techniques, Golden Chains is a pattern-matching technique (like XY-Wing), and does not feel so much like a fishing expedition, or guessing. [...]

February 20th, 2006 at 1:43 pm

[...] I am currently at a level where I can solve all easy and intermediate Sudokus, but I still have some problems doing the hard ones, so I was looking for Sudoku solving strategies on the web. KrazyDad happens to have a good overview. [...]

March 21st, 2006 at 3:01 pm

Thanks for this references. I will translate and update my own website with those techniques.

July 11th, 2006 at 12:50 pm

Maybe I just don’t understand the definition of “buddies”. In your example, you write that in figure 4, r1c1, r1c2, and r2c9 are “buddies” of the first and last cell of the Golden Chain. But, r1c2 contains a 9 as the correct answer. Please explain just what a “buddy” is.

Thank you.

April 10th, 2007 at 12:16 pm

At what point does reverse engineering fail?

I just fill in all numbers missing from a 9-square, then further subtract numbers existing in rows across and then again down. This usually leaves you with at least one single number, and then you can begin subtracting again. Most (80%) puzzles solve this way. The ones that don’t are the ones with two pairs which force you to choose one of the pair (guessing) and then go from there. You have a 50% chance of solving your first try. Then there are the really tough ones that don’t even give you that option and I have not determined any way to solve these. I.e. the “insane” ones this blog site offers.

What I would like is a simple way to solve these; any secrets or is it just guessing again? I will cross these off my list if it’s just gessing; takes all the fun out of it.

April 10th, 2007 at 12:21 pm

Some of the ones that you are currently solving using guessing don’t require guessing – e.g. you can use XY Wing or other strategies instead of guessing. However, the insane ones on this site do require some guesswork.

- Jim

April 10th, 2008 at 2:39 pm

For more strategies in one place, try http://www.sudoku-strategies.net.

November 2nd, 2008 at 3:27 pm

I am very new to Sukoku, but am already addicted, and have fairly quickly gotten to where intermediate puzzles are no huge challenge. I’ve been working on a hard one, and gradually have made headway, as I have begun trying to master some of the various techniques. But I got totally stumped just a few steps short of the point at which everything solves easily. I refuse to guess or try to play an extended option to see if it eventually causes a contradiction, because what’s the fun or challenge of that? So, I was totally thrilled to stumbe on this website, with its link to the website for learning Golden Chains. I was at the point of a large number of the kind of cells with just two options remaining in each that the technique uses, and sure enough, I found one Golden Chain that unlocked one cell, and the puzzle was trivial from there. Thank you, that was just the technique I needed.

July 3rd, 2009 at 6:10 pm

Katesisco mentions above on April 2007 a system of subtracting numbers that I don’t understand. Can you please explain it. Thanks, Ed