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## Ambiguity

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Ambiguity - 10/6/2013 11:02:07 AM
Mondobone

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Joined: 2/7/2012
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Puzzles only have one solution, right? Does that mean any option where the selection is ambiguous is wrong by default? Let me post an example from the nurikabe I'm working on right now.

In the circled area with the seven, it needs to extend one additional space. But if it extend to any portion of the strip on the right it'll have the same result on the rest of the puzzle. All the other white portions of that strip get filled in and form a broken line. Does this mean that none of those spaces can include a dot since if one of them did the other similar spaces would come out to be identically plausible?
RE: Ambiguity - 10/6/2013 5:44:11 PM
dave

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From: Israel
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Your explanation is correct. You don't fill (or mark) a square because you can, but only because you must. In the area you described, any of the empty squares *might* contain a dot so you cannot make a step in that area right now.

Thanks, Dave

RE: Ambiguity - 10/6/2013 6:29:47 PM
Mondobone

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Joined: 2/7/2012
From: United States
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That's not quite what I meant, though. I mean that no matter what happens anywhere else in the puzzle, four of those squares will remain unsolvable. Just as an example take the two bottom most blank square there. If you put a dot in the bottom one, the four above it would have to be darkened. The four above it would not connect to the line below it. If you instead put a dot one space above that, you would fill in the three spaces above and one space below, which wouldn't have an effect on the rest of the puzzle. Those two spaces are permanently ambiguous. Does this mean that they cannot be the logical answer to the puzzle?

RE: Ambiguity - 10/12/2013 2:08:58 AM
hok0003

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Joined: 1/14/2012
From: Australia
Status: offline
If you assume there is a unique solution, then yes, you can eliminate ambiguous possibilities.

Personally, I don't make that assumption. It isn't strictly in the puzzles' rules, and if there is a unique solution then it can be solved without that assumption.
Also, some puzzle sources aren't as rigorous in ensuring uniqueness.

It is a good place to start a trial and error process from though.

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