Re: The Ultimate Sudoku Challenge (Will Shortz)


Mark P wrote:
Phil Knox wrote:
exactly...there HAS to be a logical solution...not one that is hit and
miss or one that involves guessing!

Phil


I'm not much into Sudoku so this may be a naive question, but isn't the
notion of solving a puzzle "with logic only and without guessing" not
well-defined? How do you decide what deductive steps count as logic or
guessing.

Just as an example, the XYWing method that was recently described in
another thread: you can call this logic if you like but to me it's more
like a situation where guessing yields only one possibility, but which
is now recognized as a pattern so that the guessing is subsumed by the
"logic".

And so it seems to me that any situation that one might ever call
guessing could subsequently be distilled into a "pattern" with
corresponding "logic" solution. (Of course this can be taken to the
extreme and every solvable Sudoku can be called a unique pattern with
its corresponding solution called the logical approach.)

So maybe what I really mean to ask is: what is the limit of Sudoku
solving methods which aren't considered guessing and how was this limit
defined?

Mark

The main difference I see between something like the XY pattern and
"true
guessing" is that with the XY pattern there is a specific pattern that
I am looking
for, and if I find it, the logical chain guarantees a contradiction in
a finite number of
steps. With "true guessing," I have nothing better to do than plunk
down a number,
and grind through until I reach a contradiction or solve the puzzle,
but I have no
idea how long it will take to reach a contradiction.

Nevertheless, I agree that it is not, strictly speaking, well-defined
when a method is
"logic," and when it constitutes "guessing"; I think it's a sort of "I
know it when I see it"
distinction. Admittedly, an idiot savant who could immediately process
all the
implications of a tentative choice in their head, and see that it led
to a contradiction,
might view what I quickly process what I see as a tedious guess as
quick and
sophisticated pattern recognition.

Momo

.

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