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In the query Five Slitherlinks, the querent means that “every [Slitherlink puzzle has] a novel resolution”. I’m newly studying about Slitherlinks, however I do not perceive what makes an answer “distinctive”. Further, one reply receives commentary that one way or the other its resolution offered is not distinctive.

Most different types of puzzle I’m conversant in discover the puzzle itself to have the burden of making certain there is a distinctive resolution, and I’m undecided what this request means on this circumstance.

So what does it imply when Slitherlink puzzles want distinctive options?

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As in lots of grid-deduction puzzles (and for that matter well-posed logical deduction puzzles of all types), you may often deduce the answer by pure logic from the given preliminary circumstances. The reality you can deduce it exhibits that it is distinctive, in any other case you’d discover a couple of chance.

If such a puzzle would not have a novel resolution, then it is arguably not a well-defined puzzle – identical to a riddle whose verses might equally effectively describe a couple of totally different factor.

For instance, let’s think about the upper-right quadrant of the Five Slitherlinks puzzle:

Initial state

  • There have to be precisely two stuffed segments adjoining to the quantity “2”. We know D2-E2 cannot be stuffed because it’s adjoining to a “0”; neither can E2-E3 since then one of many segments adjoining to the “0” must be stuffed. So we will fill D2-D3-E3 immediately. From D2, the slithering hyperlink cannot go to D1 or E2 due to the “0”, so it should go to C2. From E3, it could actually’t go to E2 due to the “2”, so it should go to E4. So far we have now:

    First four segments filled

  • From E4, the slithering hyperlink cannot go to E5, as a result of then it must go to D5 and violate the “1”, so it should go to D4. From D4 it could actually’t go to D3 as that will shut the loop too early, or to D5 due to the “1”, so it should go to C4.

    Next two segments filled

  • There have to be precisely one empty phase adjoining to the “3”, and it have to be both C3-C4 or B4-C4 since we will not have each of those stuffed. If it is B4-C4 that is empty, then the slithering hyperlink goes C4-C3-B3-B4, finishing each the “1” and the “3”, after which there isn’t any option to make it join up:

    Contradiction

    So the slithering hyperlink should go C4-B4-B3-C3, after which it is clear learn how to end off:

    Final solution

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