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#1: Jan Wolter (jan) on Dec 29, 2008

Boring image, but slightly interesting to solve.

Slightly is being a gentleman as Jan is always ....

My best friend, who introduced me to this site, his girlfriend and I were having a discussion on what constituted "some guessing" when a puzzle was "solvable by logic alone" and/or had a "unique solution."

The basic argument was that if a puzzle had some sort of "unique solution" then it should be "solvable by logic alone" because no other combination of solutions would solve the puzzle.

The best argument we could come up with that a puzzle might have a "unique solution" and still require "some guessing" was that if coming to the solution required some quantity of trial and error or to look more than a few moves ahead to determine what the solution might be then it "required some guessing" while still being unique.

This puzzle sort of demonstrates that argument. The bottom is easily solvable without any trial and error or looking ahead. However, the last 3 to 4 rows at the top required looking a move or two ahead to see that if one combination were used instead of the other than the row above it would not be solvable.

Other than all of the convoluted over-thinking above it the only redeeming quality (let me qualify - "for me") of this puzzle. Otherwise -WOT.

I disagree, Martin. There is absolutely no guessing or looking ahead. The outside 1s of the upper 1 1 1 1 row can be placed immediately which gives you the 1s you need for 1 1 columns. Then you have the exact amount of space you need for the 1 2 1 row. After that it's all about filling the blanks.

This puzzle is definitely solvable by pure line solving (looking a one row or column at a time). Even the somewhat dim-witted "helper" can solve it without help. What makes the puzzle "slightly interesting" is that the way forward isn't always obvious to human eyes.

However, yes, the term "logically solvable" is used here in a sense more narrow than the strict mathematical sense. In the strict mathematical sense, any puzzle with a unique solution is logically solvable. The following logical procedure will work: (1) Generate every possible combination of black & white cells, (2) Check them all against the clues, (3) the one that works is the correct solution. So, yeah, lots of things are logically solvable in this sense, but who cares? We are looking for things that make elegantly solvable puzzles.

Hmmm...I almost like that. "Elegantly solvable" instead of "logically solvable". But that would open up a whole different set of arguments.

So I've got several definition of "logically solvable" as applied to this site, which I think are all pretty much similar: (1) Solvable without substantial backtracking, (2) solvable in ink, and (3) solvable using only the solution techniques covered on the "Advanced Puzzle Solving Techniques" page, and other similar methods.

No guessing or trial and error. Merili stated what I was going to write.

Once again, what does the title has to do with anything ?

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i'm a newbie, and it was line solvable to me

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