scott <sco### [at] scottcom> wrote:
> Isn't trial and error a form of deduction anyway?

  The most common aid used in solving sudoku (and thus supported by most
sudoku software) is to put small marks like "in this 3x3 subgrid a 5 goes
to either this square or this one" (by writing small 5's at the corner of
the square) and the like. I don't call that "trial and error", but a form
of bookkeeping. You are simply marking what you can deduce (ie. which
numbers must go where). At some point when you solve parts of the rest
of the puzzle, you'll end up seeing in which of the two squares the 5
really goes.

-- 
                                                          - Warp

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Warp wrote:
>   That's the marvel of sudoku: There's only one solution,

I think it's possible (trivial, even) to create a sudoku puzzle with 
multiple solutions quite easily. You have to trust the people generating the 
puzzles to ensure they're unique. If the creator hasn't done that, then you 
wind up with a sudoku puzzle with multiple solutions. Whether you still want 
to call that Sudoku or not (or just call it "like sudoku, but with multiple 
correct answers") is another question.

Conceivably, even crossword puzzles might have multiple solutions, altho 
it's far less likely.

-- 
   Darren New, San Diego CA, USA (PST)
   "Ouch ouch ouch!"
   "What's wrong? Noodles too hot?"
   "No, I have Chopstick Tunnel Syndrome."

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Darren New <dne### [at] sanrrcom> wrote:
> Warp wrote:
> >   That's the marvel of sudoku: There's only one solution,

> I think it's possible (trivial, even) to create a sudoku puzzle with 
> multiple solutions quite easily.

  I don't think anyone doubts that. In fact, creating a good sudoku with
a unique solution is probably the hard part.

> You have to trust the people generating the 
> puzzles to ensure they're unique. If the creator hasn't done that, then you 
> wind up with a sudoku puzzle with multiple solutions. Whether you still want 
> to call that Sudoku or not (or just call it "like sudoku, but with multiple 
> correct answers") is another question.

  I'd call it a poor sudoku puzzle. :)

-- 
                                                          - Warp

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Warp wrote:
> Darren New <dne### [at] sanrrcom> wrote:
>> Warp wrote:
>>>   That's the marvel of sudoku: There's only one solution,
> 
>> I think it's possible (trivial, even) to create a sudoku puzzle with 
>> multiple solutions quite easily.
> 
>   I don't think anyone doubts that. In fact, creating a good sudoku with
> a unique solution is probably the hard part.

OK. It just wasn't clear whether you were saying it *does* have only one 
solution, or *should* only have one solution.

-- 
   Darren New, San Diego CA, USA (PST)
   "Ouch ouch ouch!"
   "What's wrong? Noodles too hot?"
   "No, I have Chopstick Tunnel Syndrome."

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On Mon, 26 Jan 2009 16:30:34 -0500, Warp wrote:

> Jim Henderson <nos### [at] nospamcom> wrote:
>> No, it wasn't broken.
> 
>> How many different possible solutions are there for filling in a Sudoku
>> if no spaces are filled in?  Now fill in 6 of the spaces.  How many
>> unique solutions result in numbers in those pre-filled conditions?
> 
>> Logically, it *has* to be possible to come up with multiple solutions,
>> otherwise there would only be *one* way to fill in the boxes to start
>> with.
> 
>   If there were multiple solutions to sudoku puzzles, it would be
> impossible to give an answer, like most sudoku magazines have: The given
> answer would only be *one* of the solutions and wouldn't really help.

Some of the articles I've read have suggested that a puzzle with more 
than one solution is generally considered "broken" or "nonstandard".  
Nevertheless, those configurations do exist, and in electronic games, 
they do turn up.

Jim

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On Mon, 26 Jan 2009 18:40:30 -0500, Warp wrote:

>> You have to trust the people generating the puzzles to ensure they're
>> unique. If the creator hasn't done that, then you wind up with a sudoku
>> puzzle with multiple solutions. Whether you still want to call that
>> Sudoku or not (or just call it "like sudoku, but with multiple correct
>> answers") is another question.
> 
>   I'd call it a poor sudoku puzzle. :-)

Ah, but you *would* call it a Sudoku puzzle nonetheless. ;-)

Jim

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>> Isn't trial and error a form of deduction anyway?
>
>  The most common aid used in solving sudoku (and thus supported by most
> sudoku software) is to put small marks like "in this 3x3 subgrid a 5 goes
> to either this square or this one" (by writing small 5's at the corner of
> the square) and the like. I don't call that "trial and error", but a form
> of bookkeeping.

But then at some point, you are going to think to yourself - if I put the 5 
in this box, that means a 7 must go in that box (maybe some more steps here) 
nope that doesn't work, therefore the original 5 must go in that other box. 
Isn't that trial and error?

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scott <sco### [at] scottcom> wrote:
> >> Isn't trial and error a form of deduction anyway?
> >
> >  The most common aid used in solving sudoku (and thus supported by most
> > sudoku software) is to put small marks like "in this 3x3 subgrid a 5 goes
> > to either this square or this one" (by writing small 5's at the corner of
> > the square) and the like. I don't call that "trial and error", but a form
> > of bookkeeping.

> But then at some point, you are going to think to yourself - if I put the 5 
> in this box, that means a 7 must go in that box (maybe some more steps here) 
> nope that doesn't work, therefore the original 5 must go in that other box. 
> Isn't that trial and error?

  No, trial and error is thinking "I don't know if the 5 goes into this
box, but I'll put it anyways to see if it works" and then later if it
doesn't work you erase it.

-- 
                                                          - Warp

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>> But then at some point, you are going to think to yourself - if I put the 
>> 5
>> in this box, that means a 7 must go in that box (maybe some more steps 
>> here)
>> nope that doesn't work, therefore the original 5 must go in that other 
>> box.
>> Isn't that trial and error?
>
>  No, trial and error is thinking "I don't know if the 5 goes into this
> box, but I'll put it anyways to see if it works" and then later if it
> doesn't work you erase it.

I don't see the difference between what you just said and what I said... oh 
well.

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scott <sco### [at] scottcom> wrote:
> >> But then at some point, you are going to think to yourself - if I put the 
> >> 5
> >> in this box, that means a 7 must go in that box (maybe some more steps 
> >> here)
> >> nope that doesn't work, therefore the original 5 must go in that other 
> >> box.
> >> Isn't that trial and error?
> >
> >  No, trial and error is thinking "I don't know if the 5 goes into this
> > box, but I'll put it anyways to see if it works" and then later if it
> > doesn't work you erase it.

> I don't see the difference between what you just said and what I said... oh 
> well.

  The difference is in the "if". When you think "if I put 5 here, then..."
that's deduction. If you think "I don't know if 5 goes here, but I'll put
it anyways", that's trial and error.

-- 
                                                          - Warp

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