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This is an entry for Fortnightly Topic Challenge #42: Wordless Connecting Walls.

Huge thanks to bobble and Deusovi for playtesting! ><
And hey, this one may also mark my 100-day puzzle here in PSE, aye-aye the golden Socratic badge! XD


enter image description here

The $16$ grid puzzles above should be divided into $4$ categories of $4$, based on some shared properties.
For the final answer, please find one or two grid puzzles that satisfy all $4$ categories!

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    $\begingroup$ Socratic badge incoming! Congratulations :) $\endgroup$ – Stiv Nov 3 '20 at 11:47
  • $\begingroup$ (never mind my comment. I'm blind ;_;) $\endgroup$ – oAlt Nov 3 '20 at 11:53
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The puzzle types are:

Yajilin, Sashigane, Star battle, Kakuro
Tapa, Pencils, Numberlink, Tents
Hitori, ABC view, Slitherlink, Battleships
Aisuban, Masyu, Herugolf, Snake

The solved grids:

enter image description here
(Note that the ABC view and the Kakuro have not been solved completely yet, since their solution is not unique)

The categories:

Already solved puzzles: Numberlink, Battleships, Masyu, Herugolf
Puzzles with 2 solutions: Yajilin, Kakuro, ABC view, Aisuban
Puzzles on a 6 by 6 grid: Tapa, Pencils, Tents, Hitori
Puzzle types starting with S: Sashigane, Star battle, Slitherlink, Snake

My final answer:

An underspecified 6 by 6 sudoku, which already has been solved! (the black digits are the original puzzle, the blue digits are filled in during the solving)
enter image description here

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    $\begingroup$ Nice going :) I was working towards a very similar conclusion but didn't know the second puzzle on the top row or the one bottom left - clearly two I now need to check out! One note: Your Tapa has a 2x2 square in it which means the solution needs a fix...! $\endgroup$ – Stiv Nov 3 '20 at 20:24
  • $\begingroup$ @Stiv You are correct about the Tapa, fixed it now, thanks! I also didn't recognize all the puzzles immediately, I have searched through a couple of lists of puzzle types to get all the names (in particular I did not know the second puzzle from row 2 and also the bottom left puzzle). $\endgroup$ – Reinier Nov 3 '20 at 20:33
  • $\begingroup$ Yup, the answer is correct, very well done! :D $\endgroup$ – athin Nov 4 '20 at 3:03
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    $\begingroup$ @athin Whoops, I guess I wasn't paying enough attention when making that puzzle. It should be fixed now! $\endgroup$ – Reinier Nov 4 '20 at 7:50
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    $\begingroup$ @Kruga see for example: nikoli.co.jp/en/puzzles/pencils.html $\endgroup$ – Reinier Nov 4 '20 at 10:04

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