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#1: Teresa K (fasstar) on Feb 24, 2010 [SPOILER]

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You will need to use what I call zigzag logic. When you get stuck, you will notice you need to place a series of 2s, with a one on the left and a one on the right, which tells you this is a zigzag rather than many blocks of 4. There is only one way to place the zigzag. Then the rest is line logic.

A fun puzzle and an interesting image!

splendid image and enjoyable solve...you were right about the zigzag. :)

Well, I'm not convinced of the validity of "zig zag logic". I can certainly see when such a zig zag solution is possible, but I can't quite convince myself that it is the only possible solution. It seems like the proof of that would have to be fairly elaborate.

Teresa I think you have to make it solvable for us to accept this entry! Sorry!

Thanks, Telly and Sally.

Jota, I think I will just withdraw this one from the contest. I don't like to edit a puzzle I have already published unless it's absolutely necessary. In this case, I kind of like it the way it is. :-) There are so many possibilities for the contest; it won't take me long to come up with something else.

Jan, if you declare this puzzle not solvable without guessing, I will accept that decision. But you said your're not convinced, so let me try to convince you. Hehehe.

I would like to point out that this type of logic was acceptable in several other puzzles here. The solution doesn't seem elaborate to me. Although you have to look a few moves ahead, it's just a matter of visually following the diagonal line to determine which direction it will go.

Here is the point where I got stuck after doing as much line logic as possible:

http://come-over.to/Play/PBN/7910a.jpg

In the shaded area (R23 C20-21), those will either be both black or both dots. The former would interfere with the row below, so they will be dots. That helps to go forward, but not far. This is where I got stuck again:

http://come-over.to/Play/PBN/7910b.jpg

When you have 1,2,2,2,2,2 one way and 2,2,2,2,2,2 the other way, you know that has to be diagonal. The question is whether it starts in the upper left or upper right (shaded). If you visually follow the diagonal, it is easy to see which way it must go. Yes, that is looking several steps ahead, but even with my terrible short term memory, it is easy to "see" without guessing. To me, this seems much easier than some of Gator's logic, which I would definitely call elaborate.

Gator, I love your elaborate logic, even when it strains my brain. :-)

I agree with Teresa on this.

While the diagonal is not inherently obvious in many cases, in this one it is clear.


The step-by-step of a staircase:

square c1r6 - c8r13

There is only a 1 in r6 and all the vertical clues in that block start with 2. Therefore this (yet unplaced) block will extend into r7.

R7 has only a 2 so the black block (still unfixed) must either extend to the left or the right. (After this step, the direction is determined as there will be a white under the first block, barring that space.)

Now, *that* horizontal block is also in a vertical 2, and since the row above is now complete, this block can only extend downwards.

And the cycle repeats, forming a staircase (or diagonal) ((or zigzag)).


The square of c19r24 - c26r30 is the same, but rotated to the right.

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Of course, even when it's not as simple as this one, it can sometimes be teased out. I just put forth some logic on this to claim that #163 is solvable. http://infrapinklizzard.deviantart.com/art/Logic-163-155347359

And the debate continues... will it ever end??? It basically comes down to this: with a diagonal or zig-zag line, is there ever a way there could be any other solution BUT the diagonal line, and/or other than the intended direction? If so, then is it truly logically solvable?

if you do some looking ahead in the bottom left region, specifically the bottom row, the two diagonal lines will solve themselves out anyways eliminating a need for 'diagonal logic'. however, you have to look 2-3 steps ahead which normally isn't logically acceptable on this site. cool puzzle still, Teresa.

Thanks, Ant.

Re #10: Adam, in many cases, there are just too many possibilities to eliminate to say that it is solvable by (human) logic, but *in this case* the 1 in row six gives a definite starting point and completely excludes the possibility of 2x2 blocks.

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Thanks for taking the time to look at this Gator. You are right, that is elaborate! And very well thought out. But that is really beyond my working memory capacity to figure out in my head without marking any squares. On the other hand, I CAN see the look-ahead moves I described in #8 very easily. My question to you is this: Is my way correct or incorrect? I've tried it twice, and it works out nicely with simple line logic once the left side diagonal is started.

I'm also going to mark this one as solvable with logic, but it definitely fits in the "unique solution, much lookahead required" category that Jan has proposed.
http://webpbn.com/read.cgi?type=T&id=215&what=allrep

Found to be logically solvable by Gator.

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Oh I love the music from South Pacific. I remember the original movie, I was only 11 or 12, and very impressionable. Our high school chorus performed all the songs from South Pacific one year.

http://www.youtube.com/watch?v=81NROmUb7o0

i enjoyed solving this :-) very nice image, also.

Fine puzzle. No rating from me on solvability, when a puzzle gets very complicated (for me, that's pretty much anything beyond simple line logic) I almost always guess. Have to admit I guessed quite a bit in this one, but I did see the diagonals and followed them.

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