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Uniqueness based methods, are they allowed?

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Do you agree with the use of solving techniques which presume a unique solution?

Yes, always

10%

[ 1 ]

Only when I trust the maker of the sudoku

30%

[ 3 ]

Only after my program has validated the sudoku

30%

[ 3 ]

Never

30%

[ 3 ]

Don't know or no opinion

[ 0 ]

Total Votes : 10

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Ruud
Site Admin

Joined: 17 Sep 2005

Posts: 708

Location: Netherlands

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Posted: Sun Feb 19, 2006 10:10 pm Post subject: Uniqueness based methods, are they allowed?

I will first show you a quote by Angus, in another topic:

angusj wrote:

Since I did mention 'Uniqueness' above, perhaps I'd better clarify my feeling on that. It is a very clever technique which is reasonably simple and seems prevalent enough to be quite useful for difficult puzzles. However, it does require the presupposition that a puzzle has a single solution, something I personally find less than satisfying as to me part of the charm of solving Sudoku is to prove there is just one solution.

This is a clear opinion. You can see the poll question, but replies to this topic with your motivations are also welcome.

Here is my opinion:

When I know the source of a sudoku is reliable, or when I tested the sudoku with my backtracking solver, I just know there is a unique solution, and there is no need to prove it. My task as a player is to find it, not to prove it.

One of the regular players of my daily nightmares asked me a very strightforward question here to be ensured he could use these techniques. For him, asking this question was part of the solving process. Many sources of sudokus guarantee that their sudokus have a unique solution that can be found with logic.

Here is an analogy: When I buy a car with ABS, traction control, airbags all around and dozens of other safety features, would I be wrong if I took a little more risk driving it, assuming that these safety devices will work?

So, using uniqueness tests and BUG variations are nice shortcuts, but with a warning sign "Use at your own risk!". I would certainly not keep them away from my users. In SudoCue, I've added an option that allows the user to choose whether or not to use them.

Ruud.

angusj
Site Admin

Joined: 18 Jun 2005

Posts: 406

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Posted: Mon Feb 20, 2006 12:00 am Post subject: Re: Uniqueness based methods, are they allowed?

Yes, this is purely personal preference the same as "backtracking" is personal preference.

fermat

Joined: 05 Feb 2006

Posts: 25

Location: Melbourne

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Posted: Mon Feb 20, 2006 3:16 am Post subject: Another option on the poll?

I would use it before guessing but after everything I usually do gets no further. If it goes wrong? Caveat emptor!

Carcul

Joined: 29 Dec 2005

Posts: 50

Location: Coimbra, Portugal

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Posted: Mon Feb 20, 2006 9:21 am Post subject:

Ruud wrote:

When I know the source of a sudoku is reliable, or when I tested the sudoku with my backtracking solver, I just know there is a unique solution, and there is no need to prove it. My task as a player is to find it, not to prove it.

But by using Uniqueness you are not proving that the puzzle has only one solution! You don't need to do that because you already know that it has only one solution. Uniqueness is a logical argument that make use of the fact that the puzzle has only one solution. What is wrong with that?! Now, if someone don't find this technique "elegant" that is ok, but "elegance" is a subjective issue. Personally, I find a solution based on Uniqueness very elegant. When solving a puzzle, if you use Uniqueness you are not proving that it has just one solution, you are simply being clever by making use of that fact.

AngusJ wrote:

It is a very clever technique which is reasonably simple and seems prevalent enough to be quite useful for difficult puzzles.

First, sometimes it is not that simple to apply (I am thinking in the very advanced applications of Uniqueness, like Almost Almost Unique Rectangles, Almost Almost Unique Loops, and others Almost Almost Unique Patterns), and second, it can be not only usefull with difficult puzzles but also with extremely difficult puzzles.

Ruud wrote:

So, using uniqueness tests and BUG variations are nice shortcuts, but with a warning sign "Use at your own risk!".

And what is the risk?? The only "risk" that I can see is the one of getting a shorter and more elegant solution. But, of course, this is just a personal opinion.

Carcul

evert

Joined: 30 Aug 2005

Posts: 68

Location: Amsterdam

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Posted: Mon Feb 20, 2006 11:35 am Post subject:

Maybe one could create a puzzle with more solutions where uniqueness tests force into one specific solution:

Quote:

This puzzle has one unique solution if and only if it has one unique solution.

Ruud
Site Admin

Joined: 17 Sep 2005

Posts: 708

Location: Netherlands

Items

Posted: Mon Feb 20, 2006 1:36 pm Post subject:

evert wrote:

Maybe one could create a puzzle with more solutions where uniqueness tests force into one specific solution

When you apply uniqueness based methods on a sudoku with multiple solutions, it either leads to one of these solutions, giving the false impression that there is a single solution, or it leads to the false conclusion that the sudoku has no solution at all, because you end up with contradictions.

I've seen both happen several times.

Check this definition:

Wikipedia wrote:

Inference is the act or process of drawing a conclusion based solely on what one already knows.

We are using inference to solve sudokus. No argument about that. So, when I know there is only one solution, then I should be allowed to use that knowledge in my reasoning.

Ruud.
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