Puzzle Description:

Skull and cross bones

#1: Norma Dee (norm0908) on Aug 1, 2017 [SPOILER]

Interesting. A skull with ears?

I wasn't able to do this one with line logic alone, but relying on the obvious symmetry got me started. I'm no good at anything beyond the simplest logic here though, so with me being one of only two solvers so far I may have skewed the rating temporarily. I wonder how it would work if the blank rows and columns were left out... (Hey Norma, isn't your comment a spoiler?)

I think the "ears" is just a way of making the curvature of the skull. When the clues are exactly symmetrical, the picture has to be symmetrical as well, so you can fill in all the middle columns.

Well, this makes me jolly, Roger. Or is it poison?

There's always been some debate whether "symmetry" counts as a valid solving technique on this site, though I believe the guideline for an official guessing/no guessing ruling is that it doesn't count. Using symmetry, this is a pretty easy solve. Without it, I'm not seeing a way to solve using moderate lookahead.

Too much guessing. I really think a slightly larger puzzle would have made a better and more doable image,
.

While I personally find symmetry to make a puzzle a bit less interesting to solve because it takes away from the joy of conquering the logic, we as humans have the brain capacity to recognize such things as symmetry in a puzzle. Since it is in our arsenal of mental capabilities, why not use it? Therefore, it is valid as moderate lookahead. In short, we can, so why not?

I wish I knew where Jan's explanation is, but if I remember right it has to do with the fact that just because clues are symmetrical doesn't mean that it's solvable...puzzles with multiple solutions for instance. I think that's why, from a logic point of view, it isn't a reliable technique.

That being said, I'm still searching for a path on this one.

If someone can show me a puzzle where the clues are exactly symmetrical and the solution is not symmetrical I will believe that symmetry is invalid. Until then I maintain that it is a perfectly logical solving strategy.

Jan discussed symmetry in his FAQ section. Click on FAQ then on Advanced Puzzle Solving Techniques and scroll down a tad to find one of his discussions. I remember seeing others but I don't remember where.

I can easily show you a puzzle with symmetrical clues that doesn't have a symmetrical solution...it just won't have a unique solution and therefore not solvable by definition, which is what I said.

No, David. If the clues are symmetrical the solution is symmetrical. It may be corner to corner symmetry, in which case it has multiple solutions, but it is symmetrical. And it can be argued that if there are multiple solutions it's not a valid puzzle, though I admit, there are invalid puzzles on this site.

Everybody is free to use whatever techniques they want, all I'm saying is that the guidelines for ratings on this site should follow the guidelines for what constitutes the various levels of logic. Otherwise, it's too subjective and therefore meaningless.

And for the record, I can make a puzzle with zero symmetry about any axis...horizontal, vertical, diagonal, etc...AND without rotational symmetry, that is clue-symmetric (and multiple solutions).

I think if I'm going to start marking puzzles that require symmetry to solve, then I would want another designation beyond "moderate lookahead" or "deep lookahead". I would want it to say something like "requires symmetry to solve". I wouldn't like it to say "logically solvable" as part of the designation as we are using our "brain capacity" to see symmetry which humans are really good at. But there is not a way for me to directly use the clue numbers to approach these logically. I would be using the pattern that we all have noticed when the clues are symmetrical.

I have searched the internet countless times hoping that I could find where someone had provided a proof for unique solution puzzles with symmetrical clues. But I have been unable to find one.

I'm going to leave the Solvability on this one alone for now. I've been able to get quite a few blacks and dots with some moderate and deep lookahead, but I haven't been able to finish it. I'm going to come back to it later.

Taking another stab at this one, starting with the moderate lookahead.

After initial line logic, EL on R3 makes R3C1-4,16-19 dots. LL.

R4C4 and R4C16 are dots with EL.

No matter how you place the 2 clues in R4, R5C2,4,6-14,16,18 always are dots.

EL on R5 makes R5C7-8,12-13 dots.

EL on R23 makes R23C1-2,18-19 dots.

El on C1 makes R18C1 a dot. Likewise, R18C19 is a dot.

Now for some deep.

If R19-21C1 is black, this forces R22C1 to be a dot and R19-20C2 black. That in turn makes R22C2 black (the 1 clue is forced from C2). Finishing the 3 clue in R22 and the corresponding dots, we will see that there is no way to complete the 2 clue in C3. So R18C1 is a dot. The same logic in C19 makes R18C19 a dot. LL.

If R13-15 is black, this forces R13C4 to be black, and R14C4 and R13C6 to be dots. That forces both R12C4 and R12C6 to be dots making R12 invalid. So R13C1 is a dot. The same logic makes R13C19 a dot. LL. (And don't miss how R13C6 has to be part of either the 4 or 3 clue in C6 making R14C6 black, likewise R14C14 black by same logic.)

I think I am stuck at the same place I was 4.5 years ago. I cannot find a logical way forward from here. I am going to mark this one as guessing then (since we do not a requires symmetry to solve category).

Found to require some guessing by gator.

I'll add a "requires symmetry to solve" designation to my list of upgrades to the site. Someday I'll have a chunk of time to work on those!

Thanks Valerie. I think we should only use that designation for puzzles that have a unique solution though. If the puzzle is a multiple solutions puzzle, then they would continue to be marked as guessing.

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