What is "guessing"?

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What is "guessing"?

Beitragvon Dev_Null » Dienstag 3. August 2010, 19:46

Hello All,

There is something that I've never quite understood - with sudokus or str8ts - that came up again the other day; what exactly is the difference between "guessing" and logic. Ulrich over in the comments at str8ts.com mentioned these forums as someplace where people might be able to help me out.

Now some things I do in solving a str8t are obviously - to me - logic, but up the other end of the scale by pure guesswork, it seems to me like the difference is often primarily in the way my mental monologue runs. Let me use a simplistic example.

If I have 2 adjacent boxes for which I've worked out all of the possible values to be:

46 | 789

Then if I say to myself "Well everything on the right is too high, so the left one can't be 4, so it must be 6." That feels like a (short, simple) chain of logic to me.

But if instead I say to myself "Lets try 4 on the left. None of the options on the right work. Try 6 then; 7 works on the right. Must be 6 and 7 then." This seems like guessing.

But the way my mind really works is: "*beat* Oh. 6 and 7. duh." Which is that? Guessing, or not? Is the only difference between the two whats running through my head as I fill in the boxes?

It gets worse (at least with sudoku) when I learn a new pattern - like an X-wing, for instance - and its explained to me in terms of trial-and-error (from http://www.sudokuwiki.org/X_Wing_Strategy): "Well, A and B are a locked pair of 6's. So is C and D. They are locked because they are the only 6's in the first and last rows. We know therefore that if A turns out to be a 6 then B cannot be a 6, and vice versa. Likewise if C turns out to be a 6 then D cannot be, and vice versa."

That clearly sounds like trial-and-error to me; we try A as 6 and see what happens. Then we try C as 6. So if I discover the consequences of a pattern by trial-and-error, and later I just recognise the pattern and apply the consequences by rote, am I using trial-and-error at that point? Even worse, what if the person who found the pattern _didn't_ use trial-and-error to discover it, but used trial-and-error to explain it to me? Am I using trial-and-error now?

It seems very confusing and blurry to me, which is why I am always unsure of what is meant when people post things like "did it in 15 minutes - no guessing." I'm not sure if anything I'm doing is guessing or not.
Dev_Null
 
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Re: What is "guessing"?

Beitragvon Ulrich » Mittwoch 4. August 2010, 18:04

Hello Dev_Null,

your question is potentially the beginning of a very long discussion. And finally it might end with an "it depends".

I already wrote some thoughts about logic and guessing at the end of my "Solver Strategy" text.

A possible definition could be based on a solver program: "Logic" means that a solution results from a straightforeward procedure, which is implemented in the code (or in your brain).

Take the example 46 | 789:

The compartment check calculates a range of this 2-straight: min is 6, max is 7, therefore 4, 8 and 9 are to be excluded. 6 | 7 is the solution. ->logic
The same result would be achieved with 456 | 789.

The solver program doesn't need to apply further procedures. A human brain might recognize the "stranded digit" situation. The 4 can be excluded, because there is no 3 or 5.

Your sudoku example, the X-Wing, is a kind of specific structure or pattern, which can be looked for and recognized. Therefore, if somebody knows the pattern of an X-Wing, he will consider that as a logic, somebody else not knowing the X-Wing pattern will call the same situation a "guessing" one.

Therefore: it depends!
Ulrich
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Re: What is "guessing"?

Beitragvon Dev_Null » Mittwoch 4. August 2010, 18:44

Aha! Well, at least I'm not the only one who finds it a fuzzy topic...

To tell the truth, I find it hard to apply the term "logic" to the recognition of a pattern and rote application of its consequences. There is logic in working out the pattern in the first place - inducing general theory from specific examples - but there is nothing particularly inductive or deductive about applying it; pattern recognition seems closer to the right term.

Thanks for your insight,
Dev_Null
 
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