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Knowing that there is only one solution is useful?

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  • Knowing that there is only one solution is useful?

    Partially solved grid included as an example, here: https://www.use.com/OhzMo
    (I tried inserting the image here directly, but it doesn't work properly. It automatically scales down so much as to be illegible.)

    Just curious: Do you do this? What would you call it?

    I've solved as far as the top grid. And I reread clue 12, which tells me Wiota Woods sells for less than Abby's Mart.

    I ALSO know that:
    No other clues refer to Wiota Woods.
    No clues refer to Upland Woods.

    Now I think: If Upland Woods also sells for less than Abby's Mart, in the final answer, I'd always be able to swap the positions of Upland and Wiota and still satisfy all the clues. I know the puzzle has only one solution, and so Upland Woods cannot sell for less than Abby's Mart.

    So sometimes, a lack of clues about a parameter can be a hint in itself.

  • #2
    It can be a hint, yes. I sometimes have found something like this and entered the information.

    On the other hand, for the puzzles that I've solved, this has never helped me at all. That information isn't built upon. It is information that otherwise would have been one of the last things chartedóbut figuring it out this way is much slower!

    I'd be interested in knowing if you've come across any puzzles where this is actually helpful.

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    • #3
      Very interesting!

      I have occasionally seen shortcuts that can be taken because of the knowledge that there is only one solution. I never screenshotted one, but your example is excellent!

      I think that seeing such shortcuts is extremely difficult. If you are playing easy or moderate puzzles, they don't ever seem to be useful. Just solving it as intended is faster. But in very few of the challenging puzzles, these shortcuts can actually be useful.

      I feel like there is no harm in using them. Certainly other people do. In the rare case that I can take advantage of such a short cut, I usually do it, if for no other reason because it is so rare, and there's a certain novel aspect to using it.

      I don't think that shortcuts like this make much of an impact on record times. For example, there are probably people that guess on the "A & B are C & D" clues, since guesses on these types of clues are right 50% of the time, and it can generate a huge shortcut if you are right. Those guesses are far more likely to affect the record times than the shortcut you are demonstrating.

      But, I'm interested in hearing what other people have to say.

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      • #4
        Originally posted by uigrad View Post
        Very interesting!

        I have occasionally seen shortcuts that can be taken because of the knowledge that there is only one solution. I never screenshotted one, but your example is excellent!

        I think that seeing such shortcuts is extremely difficult. If you are playing easy or moderate puzzles, they don't ever seem to be useful. Just solving it as intended is faster. But in very few of the challenging puzzles, these shortcuts can actually be useful.

        I feel like there is no harm in using them. Certainly other people do. In the rare case that I can take advantage of such a short cut, I usually do it, if for no other reason because it is so rare, and there's a certain novel aspect to using it.

        I don't think that shortcuts like this make much of an impact on record times. For example, there are probably people that guess on the "A & B are C & D" clues, since guesses on these types of clues are right 50% of the time, and it can generate a huge shortcut if you are right. Those guesses are far more likely to affect the record times than the shortcut you are demonstrating.

        But, I'm interested in hearing what other people have to say.
        I'm curious why you're referring to it as a "shortcut", as if it were something less than commendable. It's a very reasonable logical deduction. Granted, this is just my inference to what you wrote and you may have not meant it that way...

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        • #5
          Yes, this is a totally valid solving method. Many logic puzzles have similar "advanced" techniques like this which only work because you know ahead of time that there must be a single, unique solution to the puzzle. One such example is the Bivalue Universal Grave (BUG) technique in Sudoku, explained nicely here: http://brainbashers.com/sudokuhelpbugremoval.asp

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          • #6
            Originally posted by KeepItGoing View Post
            I'd be interested in knowing if you've come across any puzzles where this is actually helpful.
            Curious! I'm not sure I have. I usually only encounter this when I'm stuck and need a breakthrough to move on with the puzzle. Doing this (in my experience) does seem to reveal isolated information, as you suggest. That is, I'm still stuck looking for the same breakthrough.

            I'll pay better attention in future, and keep my eyes open for a counterexample! I feel like there's a mathematical answer to this lurking...

            Originally posted by uigrad View Post
            I don't think that shortcuts like this make much of an impact on record times. For example, there are probably people that guess on the "A & B are C & D" clues, since guesses on these types of clues are right 50% of the time, and it can generate a huge shortcut if you are right. Those guesses are far more likely to affect the record times than the shortcut you are demonstrating.
            You're right that it's slow. Other strategies may apply to small sets of clues, but this one requires that you review them all to confirm that information isn't there. Usually at this point, I'm stuck, and have been ctrl-F ing parameter names to hopefully match up revealing clues anyway.

            Originally posted by kgf View Post
            I'm curious why you're referring to it as a "shortcut"...
            I think 'shortcut' is descriptive in this sense: You can reveal early on information that wouldn't be fleshed out until the end of the puzzle. Skipping ahead, in some sense. Like bagging your leftovers before you finish dinner.

            Originally posted by admin View Post
            Yes, this is a totally valid solving method. Many logic puzzles have similar "advanced" techniques like this which only work because you know ahead of time that there must be a single, unique solution to the puzzle. One such example is the Bivalue Universal Grave (BUG) technique in Sudoku, explained nicely here: http://brainbashers.com/sudokuhelpbugremoval.asp
            Interesting. Them dedicated sudoku folks have serious business names for their strategies!

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            • #7
              This isn't a shortcut. This isn't even an advanced strategy. It's just common base logic. If one thing sells for less than a second, then a logical truth is that the second sells for more than the first. I'm not sure how this is more beneficial than the original statement itself. It's self-evident to the statement, not advanced deduction.

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              • #8
                Originally posted by GenLando327 View Post
                ...
                I haven't explained very clearly.

                Let's say you have two parameters in the same category: P1 and P2. For example, London and Paris in the category 'cities'. Only one clue constrains P1: London has less than 13 metro lines. None of the clues constrain P2: Paris. So we know that Paris does NOT share a similar constraint. That is, Paris does NOT have less than 13 metro lines.

                Why? If Paris DID have less than 13 lines, when you finished the puzzle, you could swap the positions of Paris and London and still satisfy all the clues. There would be no unique solution to the puzzle.

                Heh. Not sure that's much better.

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                • #9
                  Originally posted by fiddleback View Post
                  Heh. Not sure that's much better.
                  Well, it was much more clear to me this way, so thanks. I've been sort of baffled by this discussion thus far.

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                  • #10
                    Ah. I understand what you're getting at now. But I would agree that generally this information is too slow to track to be overly useful, particularly in the more advanced puzzles. Maybe as a last resort, but in my opinion, the possibility of an accidentally flawed assumption leading to incorrect things getting ruled out is too high.

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