Saturday, 17 May 2014

grid deduction - The Terrible Twos of Slitherlink Part Deux


Please read and understand my first question before proceeding. This one should be worse.



pdf files I uploaded to Dropbox:


Slitherlink of Twos


Their solutions


These puzzles were generated by computer. A good solver has no problem solving them, so I can't just ask for people to find the solutions. That's why I'm just giving the solutions to you up front. Fair warning, these are super hard to solve by hand.


I did think of a different question I could ask, but we need to define some things first.


A Slitherlink of Twos is a typical, square cell, Slitherlink puzzle where each cell is either a "2" or left blank. It may have any grid size, even rectangular ones, just nothing weird like an "L" shape. It must have exactly one loop for a solution.


Let us also define backfill as the process of, having solved a Slitherlink puzzle, going back and filling in each blank cell with the appropriate number for the solution.


As we learned from the previous question, for a Slitherlink of Twos, we would expect that when we backfill a typical puzzle we would at some point be adding ones or threes.



Can you, when you backfill any Slitherlink of Twos, add a zero to a cell?





Answer



Well, look what I found. Another shot at a Slitherlink!


Answer:



Yes, there is (at least) one solution.



Explanation:



I believe this is the only solution that will work:



Solution


The real key here is to know some of the intricacies of Slitherlink:


1. If you have one or more zeroes along the edge of a puzzle, it would necessitate ones and/or threes in the puzzle elsewhere. This means that the zeroes have to be somewhere in the middle of the puzzle. Here's a couple of examples:


Large near-solution
Larger near-solution


2. Slitherlinks can only have one loop; you cannot have concentric loops as in the following:


With these things in mind, I do not see another way to have a Slitherlink puzzle with only zeroes and twos than the one that I found. I would be interested to see if someone's found another way!


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