This is a yajilin puzzle with a little bit of a backstory. Here is where I told Chaotic I was proving NP-completeness of KenKen, and after complicatedly and inelegantly doing so, here is where he did so in a really simple and annoying-that-I-didn’t-think-of-it manner. Lastly, “My target: Prove or disprove that Yajilin is NP-complete” – Chaotic_iak.

The following Yajilin has 4 solutions, can you find them all?

So this week was a little bit experimental without the day ratings and exploring an idea rather than a theme, but I had fun making these. Also, note the double meaning in the title. The other puzzles had titles like “Seek-and-Spell and Anglers” where as this one has no second puzzle, yet this is also a Yajilin “and”. (The shaded cells could be filled with numbers pointing toward the edge or with no information, but I was lazy and they are pretty implied so…)

Note that this is not a proof of NP-completeness without crossing wires, which I was not able to manage. I found how to do shifting, turning, and copying wires, but not crossing.

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I’m getting five solutions. Place a black cell at R6C5…