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Puzzle Fri November 27th (Friday, 27th November 2020)
MondSemmel
Kwon-Tom Obsessive
Puzzles: 5258
Best Total: 7m 47s
Posted - 2020.12.02 01:02:50
After I solved this puzzle with what I figured was a very fortunate single trial & error exploration (-> second image), I looked at the day's leaderboard and saw that the solving times were very long for a Friday puzzle. Given that the puzzles on each weekday typically have a similar difficulty level, I wondered what was different this time, or why the puzzle generator considered this puzzle to be a typical Friday puzzle but us puzzlers had so much more trouble with it.

With reasonable solving techniques and patterns, and without guesses, we reach this image 1:


So after exhausting our tools of the trade, most of the puzzle remains unsolved.

At this point I figured I might as well do a trial & error exploration. But where to start, i.e. which guess seemed most likely to quickly result in a contradiction? The area in the top right seemed most fruitful, though I briefly considered the bottom right as well.

Ultimately, I figured the following guess would likely result in a quick contradiction, and therefore progress, because the loop would likely close due to the L-shaped 2-3-2 area in the center right (image 2):


Instead, following this exploration (instead of stopping early for lack of a contradiction) smoothly led to the solution.

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Why mention all this? Because I think this gives some insight into how this puzzle was considered as a typical Friday puzzle by the generator, but much harder by us puzzlers. The main challenge to solve this puzzle is not applying patterns, but instead it's about identifying where in the puzzle a piece of loop closes early (-> resulting in two separate closed loops, which violates the slither link rules) in almost all permutations.

In other words, the reason we don't get far with applying patterns and normal solving techniques (-> image 1), and the reason why the puzzle looks so tough, is because without the area in the top right which features this piece of early-closing loop, the remaining three corners of the puzzle do not have a unique solution, and therefore we can't make progress in them.

To visualize this, let's reverse the guess from image 2. As the guess lead to the solution, reversing the guess should eventually yield a contradiction. We first get this position (image 3):


The 3-clue in the center (where I've added question marks in the image) is a good candidate for a second exploration, yielding the following contradictions (images 4 and 5):



In image 4, there are two loops; otherwise the solution is almost unique. In image 5, we once again get two loops, but the bottom right is not unique.

Crucially, images 4 and 5 have few lines in common. In other words, this puzzle only has a unique solution because of the loop in the top right that closes early. Therefore, trying to solve this puzzle from anywhere other than the area in the top right doesn't work well; if you weren't fortunate enough to try guesses or explorations with the loop in the top right, solving this puzzle should take a long while.

I assume this explains the perplexing disparity in the leaderboard for this puzzle - I got pretty lucky, and after writing all this, I understand how.
Last edited by MondSemmel - 2020.12.02 01:06:05
Jankonyex
Kwon-Tom Obsessive
Puzzles: 5050
Best Total: 9m 35s
Posted - 2020.12.02 02:34:19
Thanks, top right is the answer, here's the solution

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