Backdoors

Everything about Sudoku that doesn't fit in one of the other sections

Backdoors

Postby Gorbi » Wed Apr 04, 2012 3:05 pm

Hi,

I have not a real questions, just some thoughts about Backdoors (Guessing a number, getting the Sudoku below SE 1.5) and wanna know your opinion. Well first of all, guessing must be allowed, when we allow Unique Rectangles. If a guess is right AND we know there is only one solution, we dont need to prove, that the other one is false.

If u consider SE ranking it turned out, that most Sudokus below 7.0 have at least one or two bivalue Backdoors. Thats huge, when you think about it. Most 6.x Sudokus dont have many bivalue cells, so the chance is very high that u find a backdoor, just by trying a few numbers.

Now here is my problem: A friend of mine and I, doing many Sudokus. He gives a [ed: expletive deleted] about theory. All he knows are Subsets, Intersections, x-Wing. He just solves normal "newspaper" Sudokus.
I told him, he cannot solve my 6.6 puzzles. But he did several times, and he did even faster then me. One puzzle for example it took me 2 hours to find all needed Turbot Fish, bivalue x-cycles and so on.
He just got to a dead end and tried to guess some bivalue cells. Thats how he solved it under half an hour. I thought this was just a coincidence, but it turned out, that he could solve every puzzle by that so far and most puzzles he did faster.
So why do I learn so much theory, if it is so easy even for Noobs?
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Re: Backdoors

Postby coloin » Wed Apr 04, 2012 3:40 pm

Well you wouldnt be the first to complain.
Famously the in first "Sudoku Word Championship" the american chap [ Thomas Snyder / Motris ] had done miles better than anyone in all the preceeding 9 rounds - he was outdone on the final deciding puzzle because the eventual winner "guessed" a clue and got the answer. Worse still [for him] the winner was female !

see world-championship

That said he was the only one to solve the penultimate [torroidal] puzzle.

And subsequently he has been word champion 3 times.

I think there can be a logical element to "guessing" and as you rightly say - whether you assume the puzzle is unique and valid as an aid to solving is also up to personal taste.

C
Last edited by coloin on Wed Apr 04, 2012 11:11 pm, edited 1 time in total.
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Re: Backdoors

Postby Smythe Dakota » Wed Apr 04, 2012 4:57 pm

I am wondering whether, in certain trial-and-error situations, there might be one guess which is obviously better than another. For example, maybe the "other" guess would establish a pattern which, though not impossible, is bizarre, and unlikely to come up unless the puzzle writer made a deliberate effort to make it come up.

If so, this could provide a new strategy for these short-cut artists to outsmart the purists and win tournaments. (Maybe that's what happened in the cases mentioned.)

It could also force a new strategy on puzzle writers. Include bizarre and rare patterns in such a way as to lead the short-cut artists astray.

Bill Smythe
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Re: Backdoors

Postby RW » Tue Apr 10, 2012 9:06 am

Smythe Dakota wrote:I am wondering whether, in certain trial-and-error situations, there might be one guess which is obviously better than another. For example, maybe the "other" guess would establish a pattern which, though not impossible, is bizarre, and unlikely to come up unless the puzzle writer made a deliberate effort to make it come up.

If so, this could provide a new strategy for these short-cut artists to outsmart the purists and win tournaments. (Maybe that's what happened in the cases mentioned.)

There is always guesses that are better than other guesses. Not guesses that are more likely to be right, but guesses that are more likely to advance the puzzle no matter what. If you choose your guess poorly, you might come to the conclusion that the guess was wrong and you have only eliminated one candidate before getting stuck again. If you choose your guess wisely, eliminating that one candidate will advance the puzzle a lot, possibly even solve it.

When the puzzle difficulty passes a certain threshold, guessing will be faster than looking for "pure" solutions. In tournaments I suppose they are trying to use puzzles that are not hard enough to make guessing profitable. If I recall correctly, the final puzzles could include some X-wings but not much more than that. These patterns you can still spot with a trained eye. If it gets much more complicated, it is faster to just choose a suitable guess and see if it solves the puzzle or lets you eliminate the candidate. This is true also for software. Brute force solvers are always faster than pattern based solvers.
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