## Question

Advanced methods and approaches for solving Sudoku puzzles

### Question

I'm just new to Sudoku and am liking it very much. I read the Solving Sudoku and am now up to easy. I was wondering about Ariadne's thread. It looks to me like another way to guess. You pick one and run it out. If it works, then fine. And if not, then the other has to be correct. Is that right? Or is this considered some sort of logic? Thanks, Rich
rich12545

Posts: 9
Joined: 02 June 2006

Ariadne's Thread is guessing. Whether or not you choose to do this is entirely up to you, but Pappocom puzzles do not require any form of guessing and nor do the more well constructed puzzles.

Luna
lunababy_moonchild

Posts: 659
Joined: 23 March 2005

Thank you. That's what I thought. No, I don't plan to use it at all. One of the main reasons I bought this game instead of one of the others I tried, even free ones, is the strict adherence to one solution and logic.
rich12545

Posts: 9
Joined: 02 June 2006

People have different ideas about what constitutes guessing, but Ariadne’s Thread or proof by contradiction is just as logical as any other method of proof. Making a hypothesis, taking it to its logical conclusion and showing that it cannot be sustained is the basis of many of the techniques used here and is absolutely logical.

Multi-solution puzzles are a different story. Here you have more than one possible combination of numbers that will give you a solution and you are forced to guess between two numbers, either of which will work – that’s another kettle of poissons altogether.
emm

Posts: 987
Joined: 02 July 2005

This is very interesting. Two long term prolific posters with opposite opinions on Ariadne's Thread. I went back to Solving Sudoku and read everything over again. First, it's clear that the author is against guessing. It's also clear that he feels AT is not guessing. As a noobie it's difficult for me to have an informed opinion. But the more I read it the more I can see both sides. It's no wonder people have different ideas.

Looking at it objectively, you have two pencil numbers one of which is correct and one is not. There is no logical basis for choosing one over the other. So you pick one arbitrarily (guess) and run it out to see if it works. If it does then fine. If not then the other must be correct.

So I think whether or not it is guessing depends on the definition of guessing in sudoku. Must you have a logical reason before inputting any number? If yes, then it is guessing. If no, then it isn't and can be used as a logical method for solving a sudoku problem.

So, what is the proper definition of guessing in sudoku?
rich12545

Posts: 9
Joined: 02 June 2006

Apparantly, if you devise a way by which you would ALWAYS select/identify the candidate that could be eliminated by contradiction without running into the correct candidate.....Than that is less of guessing & more of a pattern which is an acceptable way of elimination.....

tarek

tarek

Posts: 2612
Joined: 05 January 2006

Must you have a logical reason before inputting any number?

I'm finding it hard to think of an illogical reason for inputting a number. Even something as simple as there's no 6 in this line is actually logical.

you have two pencil numbers one of which is correct and one is not. There is no logical basis for choosing one over the other. So you pick one arbitrarily (guess) and run it out to see if it works. If it does then fine. If not then the other must be correct.

If the first number works and you run with it without checking then you have guessed.
If you check both numbers and get a contradiction or if both possibilities confirm a third cell then you are not guessing.

So, what is the proper definition of guessing in sudoku?

As you say, people have different opinions on this but I would say

1. proof by contradiction (often called trial and error) is not the same thing as guessing
2. pattern identification can be considered more elegant but it's no more logical
3. guessing is inputting a candidate without checking the alternatives or
4. guessing is the choice you have to make between candidates in multi-solution puzzles
emm

Posts: 987
Joined: 02 July 2005

### define guessing ??

Pat

Posts: 3425
Joined: 18 July 2005

Bailed out of discussion!
Last edited by daj95376 on Sun Jun 04, 2006 3:16 pm, edited 1 time in total.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

First, I don't know what bifurcation means.

It looks like you find a difference between "trial and error" and "guess." I can see how you come up with this difference. You actually take two pencils and run each out to see if either leads to a logical conclusion. You look at this as no different from taking one cell and checking to see if this or that number will work. You see AT as doing the same thing but carrying it out more steps. Is this a correct assessment?
rich12545

Posts: 9
Joined: 02 June 2006

bifurcate:

To divide into two parts or branches.

I'd also like to point out, just in case it wasn't clear the first time
lunababy_moonchild wrote: ...Whether or not you choose to do this is entirely up to you....

I'm sure that I've said this elsewhere but I personally don't like AT because I can't figure out how to follow the thread back if the wrong number is chosen. In the event that there is a way of doing this it seems to me that you'd make a right mess of the puzzle.

I either get the puzzle right or I don't. I'm not an expert on the subject - of AT or logic in general, nor on sudoku - but that's the opinion I hold.

For what it's worth I didn't say that the technique is wrong I just said that it was guessing, which in my opinion it is. I suppose that you could say, in programming parlance, that it was an if..then..else statement which I was taught was a logical technique (when it came to programming computers).

Once again, it really depends on how you personally want to play the game. There is only one rule .

rich12545 wrote:It looks like you find a difference between "trial and error" and "guess." I can see how you come up with this difference. You actually take two pencils and run each out to see if either leads to a logical conclusion. You look at this as no different from taking one cell and checking to see if this or that number will work. You see AT as doing the same thing but carrying it out more steps. Is this a correct assessment?

Looks like a fair assessment to me.

Luna
lunababy_moonchild

Posts: 659
Joined: 23 March 2005

Good. Since I'm still learning the basics and getting a challenge from easy puzzles, it will be a long time before the opportunity to use AT comes up. It apparantly is used only as a last resort on very hard and up puzzles. It looks like it is in a bit of a grey area but leans to logic so I'll likely use it at that time.
rich12545

Posts: 9
Joined: 02 June 2006

emm wrote:People have different ideas about what constitutes guessing, but Ariadne’s Thread or proof by contradiction is just as logical as any other method of proof. Making a hypothesis, taking it to its logical conclusion and showing that it cannot be sustained is the basis of many of the techniques used here and is absolutely logical.

Multi-solution puzzles are a different story. Here you have more than one possible combination of numbers that will give you a solution and you are forced to guess between two numbers, either of which will work – that’s another kettle of poissons altogether.

Suppose you pick the right choice first. Using this technique is only logical if you then go on to check all other possibilities, something I doubt many solvers would do
ab

Posts: 451
Joined: 06 September 2005

Apparently, I misunderstood.
Last edited by daj95376 on Mon Jun 05, 2006 10:58 pm, edited 1 time in total.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

ab wrote:Suppose you pick the right choice first. Using this technique is only logical if you then go on to check all other possibilities, something I doubt many solvers would do

I took that to mean people and solving by hand, Daj.

Luna
lunababy_moonchild

Posts: 659
Joined: 23 March 2005

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