#1: Steve (stevieb) on Jun 25, 2020 [SPOILER]
In algebraic geometry, a lemniscate is any of several figure-eight or ∞-shaped curves. The word comes from the Latin "lēmniscātus" meaning "decorated with ribbons", from the Greek λημνίσκος meaning "ribbons", or which alternatively may refer to the wool from which the ribbons were made.#2: Philip (Philip) on Jun 25, 2020
I'm running out of logical steps pretty quickly on this puzzle. Does it require guessing?#3: Web Paint-By-Number Robot (webpbn) on Jun 25, 2020
Found to be solvable with moderate lookahead by valerie.#4: Jota (jota) on Jun 25, 2020
No Phillip, edge logic!#5: Kristen Coolman (kristen) on Jun 25, 2020 [SPOILER]
And here I thought it was going to be a pince-nez! https://en.wikipedia.org/wiki/Pince-nez#6: Kathy Cain (kathycain) on Jun 25, 2020 [SPOILER]
I too thought "pince-nez". But with "Lemniscate", I am learning a new word!#7: Belita (belita) on Jun 25, 2020 [HINT]
Edge logic doesn't quite solve it because the sevens on the ends don't pinpoint where the twos go in the next column. Also, there are three locations where the fives could go on the top and bottom. But since the puzzle is exactly symmetrical and has a unique solution, you can use symmetry to solve it. Common sense works well, too.#8: BlackCat (BlackCat) on Jun 25, 2020
Odd. I agree with Kathy.#9: Joe (infrapinklizzard) on Jun 25, 2020 [HINT]
After LL#10: Brian Bellis (mootpoint) on Jun 25, 2020 [HINT]
EL 7 c1 = r1, r11 white
EL 7 c21 = r1, r11 w
EL 2 c3 = r6 w
EL 2 c19 = r6 w
And then I see no moderate lookahead. The 5s in r1 have seven slots they could fit in (as do the 5s in r11). I can't even find any deep lookahead.
I don't see any way forward other than by assuming symmetry, which is a guess.
So if you try to put one of the 5's from the first row in the center, you eventually reach a contradiction. So the two 5s must be in columns 3-8 and 14-20. The same for the last row for the same reasons. The solve is then straightforward.#11: Bruce Yanoshek (yanogator) on Jun 26, 2020
Brian is right about the edge logic. After that, it is entirely LL.#12: Belita (belita) on Jun 26, 2020 [HINT]
Symmetry isn't a guess if you know that there is only one solution, and if there are multiple solutions it will show up as a question mark in the puzzle list. If you disagree, prove it with a single-solution puzzle that looks like it would be symmetrical, but isn't.#13: Vicki Catherine Woods (vickicwoods) on Jun 26, 2020
I just used symmetry starting with the edge 7's. Then I cascaded my 2's and 3's. It was a quick solve after that.#14: Aurelian Ginkgo (AurelianGinkgo) on Jun 27, 2020 [HINT]
Assuming symmetry , I feel, is a guess as it is yet an unproven theory either way. But I noticed what I like to call zigzag logic. I don't know if there is something to it, but whenever I see a bunch of 2s and nearby 1s in the clues, it is always a zigzag or stepladder. This may also be guessing, I admit, but so be it. It solved it for me.#15: Brian Bellis (mootpoint) on Jun 28, 2020
The tricky part is determining where to start zigging and zagging.#16: Joe (infrapinklizzard) on Jun 28, 2020 [HINT]
Disproving the center position for the 5 is at the very least deep lookahead, and it's so far ahead I certainly can't keep it in my head. So I would still class that as guessing.#17: Teresa K (fasstar) on Jun 29, 2020
Remember, if you have marked anything "temporarily" or erased anything, that is considered "guessing" on this site. The goal is to solve the puzzle as if you were solving it in ink.
Symmetry is a bit of a sticking point. All the empirical evidence points to a symmetrical puzzle with a unique solution having only one solution, but that is not a proven thing. Also, even Jan pointed out that symmetry shouldn't be counted unless the "unique solution" status were pointed out in the title.
I would argue that that is not enough, because an author could easily be lying or mistaken. The clues never are.
The 2s with the 1s next to them will not always cause a zigzag. If the 5 in r1 went all the way left, it would take care of the top 2s and 1s, and the left 2s in r2-3. That would force the 7 in c1 down to r10. That would take care of the bottom 2s on the left side. the second 2 in c3 could easily fit in r4-5 or r7-8 without immediate conflict. This is deep lookahead, and we're still stuck.
I still think this is "some guessing", but is definitely at least deep lookahead. If you want to argue for another classification, the way to do it is to give all the steps that are not line logic, like I do.
Joe, you said everything I was thinking, but couldn't put into words. Thanks.#18: Belita (belita) on Jun 30, 2020
Just out of curiosity, who puts the question marks in to indicate if a puzzle has multiple solutions? Is that part of the program or does somebody have to do that manually? I really depend on those question marks, because I don't do the ones with multiple solutions. I don't consider them legitimate puzzles.#19: Joe (infrapinklizzard) on Jun 30, 2020
Belita, generally uniqueness is determined at the time of creation. There is a program that is very competent that determines the uniqueness and solvability (LLS, anyway), but it is given a one-second time limit to avoid tying up the server. 99.9%+ are determined in that time.#20: Belita (belita) on Jun 30, 2020
If the server cannot determine whether it is a unique solution, then the puzzle is generally a complete mess to begin with.
Here's a way to be certain: if the puzzle is new and there is a box underneath that asks you to rate the uniqueness, then it is probably a bad puzzle.
The reason I say "new puzzle" is because of the puzzles from the Missing Times. They lost their ratings, so the determination has to be set manually by one of the moderators. We're working our way through slowly as we have time (and ambition, in my case).
PS. If the Uniqueness box is shown, choosing a selection is voting for that answer. Only a moderator can definitively set an unknown puzzle to "unique". *However*, if *anyone* comes up with a correct solution that is not the same as the intended one, the server immediately marks the puzzle as multiple-solution and puts up a comment by the webPBN Robot that says that the puzzle was found to have multiple solutions by [username]
That's great. And hat's off to the moderators who do such a great job keeping the site working.
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