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Marty R.
Joined: 12 Feb 2006 Posts: 5767 Location: Rochester, NY, USA

Posted: Tue May 16, 2006 4:50 pm Post subject: Exactly what constitutes trialanderror? 


Where does logic end and trialanderror start? To me, that line seems blurred. It’s clear that techniques such as pairs, triples, etc., wings, fish, coloring, strong links, rectangles, and the like fall into the category of logic, but it’s the chains that have me wondering.
Suppose one decides to start a forcing chain based in a twocandidate cell. Or he sees that a number can occur only twice in a certain box and decides to test for each of the possible occurrences. It seems that the actions taken from these chains are based on logic; for example, cell suchandsuch is “X” for either value, therefore, that cell must be “X.” But the deciding where to start these tests seems to have an element of trialanderror to it, unless, of course, there is some sort of logic that tells one where to start the chain.
So where do YOU draw the line? How do you define trialanderror? What does a puzzle constructor have in mind when he guarantees that his puzzles are all solvable by logic, without resorting to trialanderror? 

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TKiel
Joined: 22 Feb 2006 Posts: 292 Location: Kalamazoo, MI

Posted: Wed May 17, 2006 2:21 am Post subject: Re: Exactly what constitutes trialanderror? 


Marty R. wrote:  But the deciding where to start these tests seems to have an element of trialanderror to it... 
I used to feel that way about chains until I thought about in a different manner. Is it guessing if you look at two cells for a hidden pair and you don't find one? If you do find one is it guessing if you had to look in three cells before you found it? Is it guessing if you make a colouring chain that doesn't lead to an exclusion? Is it guessing if you see two bivalue cells and look for but can't find the third one to make an 'xywing'? Nobody questions the logic of these techniques once found but nobody asks if there was a logical reason to look for it where it was found either.
If we don't hold other techniques to an arbitrary "what logic told you to look in that cell" criteria, why should it be done for forcing chains? If we accept the logic of a forcing chain, it shouldn't really matter how it was found, any more than it does for any other technique that is used. 

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ravel
Joined: 21 Apr 2006 Posts: 536

Posted: Wed May 17, 2006 10:49 am Post subject: 


Thanks Tracy,
you have formulated, how i think about it, much better than i could 

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Marty R.
Joined: 12 Feb 2006 Posts: 5767 Location: Rochester, NY, USA

Posted: Wed May 17, 2006 3:53 pm Post subject: 


Tracy, I agree with Ravel, I don't see anything wrong with what you say. But I do frequently see references to trialanderror and am just trying to find out what people mean by it. 

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David Bryant
Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Posted: Wed May 17, 2006 5:57 pm Post subject: Defining "T&E" 


To me, "trial and error" means outright guessing  just enter a value in some cell, and try to work the puzzle. If it works out, you're done  if not, go back to the starting point and make another guess.
I think that Alan R is the only regular poster on this forum who wants to define forcing chains as "T&E". dcb 

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keith
Joined: 19 Sep 2005 Posts: 3321 Location: near Detroit, Michigan, USA

Posted: Wed May 17, 2006 8:45 pm Post subject: Subjective 


The answer here is entirely subjective, an opinion. And, sometimes used to denigrate someone else's solution technique.
What David describes is called "backtracking".
An backtracking analog is to solve a maze: Unroll a ball of string to mark your path. Go anywhere. If you reach a dead end, back up to the last intersection (with your string), mark the passage as no good, and try any other unmarked path. Guaranteed to work, but most would agree this is trial and error.
Keith 

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TKiel
Joined: 22 Feb 2006 Posts: 292 Location: Kalamazoo, MI

Posted: Thu May 18, 2006 12:15 am Post subject: 


Marty R. wrote:  But I do frequently see references to trialanderror and am just trying to find out what people mean by it. 
I don't think there is a blanket answer for that. IMO some people use the term 'trial & error' in reference to a technique or pattern that they either don't understand or one in which they don't see/accept the logic. (Which for quite a while for me was a forcing chain, until I thought about it in the terms above.) Others use the term for techniques similar to those described by David and Keith, and that seems to be the concensus on those techniques. 

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