Advanced methods and approaches for solving Sudoku puzzles

### Response to Animator

Thanks to Animator and angusj for their help.

Now I understand a "Naked" triple. The triples that I have used before are presumably "Clothed" triples where 3 candidates only appear in 3 cells but there might be other candidates in those cells.

I actually used a different on-line solver to find the solution and it came up with a quadruple of 1, 4, 8, 9 in the other 4 cells of grid 8.

Does it always happen that there is a Quadruple (or Quintuple) in the cells that don't comprise a Naked Triple (or pair)? Thinking about this logically, I believe that these two conditions are two sides of the same coin.
Art Hedgehog

Posts: 5
Joined: 12 June 2005

Yes.

If you find one group of numbers (in this case the triple) then you will always find atleast one other group. (it's ofcourse possible that you find a triple and two pairs for example)
Animator

Posts: 469
Joined: 08 April 2005

So what other techniques don't I know about?

I have seen something about "Hidden" pairs. What are these? [/quote]
Art Hedgehog

Posts: 5
Joined: 12 June 2005

I've been doing soduko's for about a week, but my work for over 30 years has involved logical thinking. I completed the rest of this problem in about 15 - 20 minutes using a long-winded (but logical) process. I guess that with more experience I would have spotted the obvious a lot quicker. I agree completely with angusj that logic is better than 'guesswork' (or SIAS as I prefer to call it). Logic is only 'complex' if ...
brifter

Posts: 3
Joined: 16 June 2005

Art Hedgehog wrote:So what other techniques don't I know about?

These sites list a variety of techniques.
http://www.sudoku.com/howtosolve.htm
http://www.simes.clara.co.uk/programs/sudokutechniques.htm
http://www.angusj.com/sudoku/hints.php
http://www.puzzle.jp/keys/sudoku_keys-e.html

Art Hedgehog wrote:I have seen something about "Hidden" pairs. What are these?

angusj's site explains hidden pairs.
scrose

Posts: 322
Joined: 31 May 2005

You are right. Let's go back to the topic.

Playing Sudoku is not only finding a solution, but it needs to be done as fast as possible. If you play the puzzle by yourself, it is find to spend couple hours to right down all pssibilities in order to find "naked pairs."

However, if you play in a group to find out who can solve the problem first. Your "naked techniques" is a slow technique.

I refers to a simple technique of "how to solve" in this Website because it can give a player get the answer faster than your "naked technique." An fifty-fifty assumption is neccessary to speed-up the process of finding a solution. The rule of playing Sudoku does not forbit about that.

I appreciate for your dedication to write your "naked technique," but my suggestion is to make things simple as it is.

Kawasaki Suzuki Susi
Sudoku Master

Posts: 6
Joined: 15 June 2005

I suggest that you should read Nishio and Trial & Error section in the Website www.simes.clara (follow the link above) to gain some more knowledge about solving Sudoku when writing your "naked technique."

Nishio Susi
Sudoku Master

Posts: 6
Joined: 15 June 2005

Sudoku Master wrote:However, if you play in a group to find out who can solve the problem first. Your "naked techniques" is a slow technique.

The "naked techniques" regarding pairs, triplets, etc. and the techniques regarding hidden pairs, triplets, etc. are simply cases of finding some combination of N numbers in exactly N cells, and thus being able to eliminate other possibilites.

It may be a slow technique to apply when searching for these pairs, triplets, etc., but there are many puzzles where you would be hard pressed to find a solution (via logic) without using that technique.

Of course, if you are solely focused on how quickly you can solve a puzzle -- as your post seems to suggest -- trial-and-error is the fastest method around. However, I believe most people aren't very satisfied by solving a sudoku by guessing.

Fixed: grammar and sloppy spelling.
Last edited by scrose on Thu Jun 16, 2005 2:50 pm, edited 3 times in total.
scrose

Posts: 322
Joined: 31 May 2005

Sudoku Master

Posts: 6
Joined: 15 June 2005

Sudoku Master wrote:
However, if you play in a group to find out who can solve the problem first. Your "naked techniques" is a slow technique.

Well, I'll respectfully disagree with you there.

I find it generally a *lot* easier to spot naked double than hidden doubles and I rarely have the patience to find hidden triples and quads (without a hint ) as they are generally so much harder to spot.

As to your suggestion that I look at Nishio - thanks, I'm quite familiar with that technique too, but I'm really only interested in *logical* solutions.
angusj

Posts: 306
Joined: 12 June 2005

Logic itself suggests that there is pretty much always 'more than one way to skin a cat'. Therefore, there will be techniques other than the purely logical route, some of which will work better/faster than others, but it's a case of horses for courses and depends on the way your mind naturally (or by training) works best. A combination of techniques gives a better toolkit. Games such as Sherlock are more pure logic, whereas Soduko opens the door to a wider audience.
brifter

Posts: 3
Joined: 16 June 2005

May you help me to use pure logic to solve the puzzle bellow?

1 2 4 | 5 8 6 | 7 9 3
8 3 7 | 1 _ 9 | 6 _ _
6 5 9 | _ 3 7 | 8 _ 1
-----------------------
9 1 2 | _ _ 8 | 3 6 _
5 4 3 | 6 1 2 | 9 7 8
7 6 8 | 9 _ 3 | 1 _ _
-----------------------
4 8 6 | 3 9 5 | 2 1 7
3 9 5 | _ _ 1 | 4 8 6
2 7 1 | 8 6 4 | 5 3 9

I do logically cannot find any logical method to finish this puzzle.

Thank you for your help "logical puree."

Nishio Shusi
Sudoku Master

Posts: 6
Joined: 15 June 2005

Sudoku Master wrote:May you help me to use pure logic to solve the puzzle bellow?

I think most people would agree that this is a poorly created puzzle because it cannot be solved by logic. Where is the joy in guessing your way to the solution? Your example also has multiple solutions. It's much more satisfying when you find the solution and you know it is the only solution.

Update: There are exactly three solutions. You can get each of them by placing one of {457} in r4c6.
scrose

Posts: 322
Joined: 31 May 2005

To be precise, the logical route is the better route to THOROUGHLY SOLVING this puzzle. If you were to make a guess, of course you would COMPLETE the puzzle, but you could make the assumption that you have found THE ONLY solution. However, if you employ logic it becomes apparent that there must be more than one acceptable answer. You then do not just make a guess or assumption, you KNOW there are three possibles.
brifter

Posts: 3
Joined: 16 June 2005

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