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

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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

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