Puzzle Description:

Answer in first Spoiler

#1: Bill Eisenmann (Bullet) on Oct 30, 2020 [SPOILER]

Bubble gum champ

Credit Roger Price

I actually guessed one!

Totally awesome puzzle!! Loved the solve. When I got as far as I could and found that nothing worked I moved the 5 across on line 4 to the extreme left and the 5 across on line 5 to the extreme right. You find that it doesn't work so I moved the top one one space and took it from there. Great solve!!!

Ailsa, it takes some internal edge logic (IEL), or 2-way logic. Look how the 5 clues flanked by 2 clues (as in C5 and C6), correspond with the 1 clues flanked by 2 clues (as in R8-R12).

After LL
EL 5 c5 = r4-6, r14-18 white
LL
EL 5 c17 = r4-6, r14-18 w
LL
EL 5 r4 = c6-7, c15-16 w
LL
EL 2s r18 = c6-7, c15-16 w
Three-way logic on the left 2 in r18 = r17c9 w
Three-way logic on the right 2 in r18 = r17c13 w


This is it for moderate lookahead. You cannot assume that the 5s are not asymmetrical - that is guessing.

The mobility of all those 2s is a big problem. Only the 2s in r5 can be pinned down to a couple positions each. However, there is no two-way logic to be had there for those positions lead to very different conclusions.

The 5 in r16 can be put in at least three positions with no conflict on crossing clues (or the ones that cross those).

I do not see a way forward in proving this.

Either assuming symmetry or assuming that the 5s make the apex of an arch will bring you to a solution, but neither will prove that that is the only solution.

(As always, feel free to provide a solution that I have not found)

Found to require some guessing by infrapinklizzard.

Doesn't require any guessing at all once you see that it's symmetrical. Draw the outer square, take out the rest of the otherwise blank rows and columns, put that top 5 in the middle of the area that remains, and the rest just falls into place. Took me only a few minutes to solve.

Yes Tom, I assumed that just by looking at the pattern of the clues you could assume symmetry.

You sophisticated solvers out there, is that a fair assumption?

Seems to be, otherwise wouldn't it be marked Multiple Solutions?

Bill, you would have to look at both the horizontal and vertical clues. If the clues in one direction, usually horizontal, are palindromes AND the clues in the other direction follow identical patterns from the outside in, you can assume symmetry. You can't assume with one direction clues alone.

I don't have the patience to test any of them, but I expect the symmetry assures a unique solution. If the pbn robot thinks otherwise, I'd like to see one such "wrong" solution. Trial and error isn't the same as guessing.

Tom, a checkerboard would have complete symmetry in both axes, but would still have two solutions.

And *for the purposes of this site* trial and error beyond a reasonable degree (what one might be expected to keep in one's head) *is* considered guessing.

[And *for the purposes of this site* trial and error beyond a reasonable degree (what one might be expected to keep in one's head) *is* considered guessing.]

I disagree. I don't apply different rules to this site than I would to any other problem. Trial and error is experimenting. If I have to start experimenting, I do so in a direction that I believe is probably wrong until logic confirms it, eventually (hopefully) honing in on the only solution that works.

Some puzzles say that guessing is REQUIRED. If you guess what you believe to be correct and get to the end, then yes, you got there by guessing, but have in no way confirmed it as the only way to have gotten there. When I post on those puzzles that guessing is NOT required, I do so because I've logically verified that there is in fact only one solution.

If a puzzle has more than one solution that meets all the criteria set out in the clues, only then is guessing required.

Your checkerboard is indeed an example where dual symmetry does NOT assure a unique solution. It does assure a really boring and annoying puzzle though.

I'll be glad to mark symmetry as not guessing once someone publishes a logical proof for it. Until then...

Definitely guessing. Agree with Gator. And if these terms aren't clearly defined for the purposes of solving puzzles on this site, then people won't know what the phrases mean for solving on this site. It's hard enough to apply words so everybody knows what to expect, let's not make them meaningless.

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