Puzzle Description:

Its a flamingo / I noticed that some puzzles labeled as some guessing required, but can be solved logically if it is assumed to be symmetrical. So i wondered if you could every logically assume a puzzle was symmetrical, this is an example of why you cant; however I was unable to make one with only one color that had only one solution. Can it be logically assumed a B/W puzzle with only one solution and has symmetrical clues must produce a symmetrical image?

#1: David Bouldin (dbouldin) on Apr 10, 2012 [SPOILER]

as i understand it, it can be logically assumed that a puzzle (B&W or color) WITH ONLY ONE SOLUTION and having truly symmetrical clues MUST produce a symmetrical image...provided that the clues on the left/vertical are symmetrical/palindromes as well.

In cases like your puzzle, where only the top clues are symmetrical and the left clues are not "balanced" in this way, the image MUST NOT be symmetrical.

nice flamingo.

I'm not a mathematician, so I don't have the tools to generate a proof, but I'm nearly certain that this must be true. The rub is that you cannot assume that any particular puzzle on this site *has* a unique solution.

As to assuming symmetry -

If the clues available are symmetrical in one direction,
AND in the other direction, all lines:
-- have an even number of clues that are symmetrical
-OR-
--have an odd number of clues where all but the center clue is symmetrical AND the "center" clue is a number that has the same parity* as the number of rows or columns in that direction,

then it's a good bet that it's symmetrical. (NB for noobs: assuming symmetry is not considered good logic on this site.)

While this puzzle shows symmetry in the column clues, the rows are beyond a doubt asymmetrical.


* -- By parity, I mean the quality of oddness vs evenness. (Eg. if the number of rows is odd, then any "center" clue for a column must then be odd if the puzzle is to be symmetrical. If the row count is even, then any column "center" clue must be even. )
-- The same idea goes in column vs row situations.

agree joe. i capitalized "WITH ONLY ONE SOLUTION" because that's a big assumption that you must know that going in, which on this site means that the creator must include this information in the title. agree whole-heartedly with your note for noobs.

David, you must have posted while I was musing. I did not see your first post until now.

It was much more succinct than mine. The only thing I added was the requirement about the matching parity of the center clue.

huh.... lol

Goto next topic

You must register and log in to be able to participate in this discussion.