Puzzle Description:

#1: Tom O'Connell (sensei69) on Jun 1, 2013

This is a toughie!

nice solve tom :)

thx Trav ... guess you figured out the 7

what is this?

Very cool,thx for the tire swing uncle sensei.:)

i solved it, but the last 10 spots or so were guessing. Cute pic.

no guessing needed, Ruby....

2-way logic...at least one of r1c11 or r2c11 must be a black. so whichever(or both) r's 1 or 2 in c 11 is black, r2c9 must be a black(take another look and you'll see why). ll takes you most of the way home from there. you come to a smile logic situation at the end with the last 2 1's in c4 and the last 2 in c5 (which you can place if you can see it, but dots r10c5 at the very least) ll finishes

good solve Tom :)

thx Kurt

I can only find deep-lookahead to get this done.

After initial line logic, simple edge logic on the 4 in r1 will dot c1-5 (otherwise it will conflict with r3).


Now we're going to have to use deep lookahead to get any further.

Extensive edge-logic on the 7 in r2. If it goes all the way to the right (c9-15) then:

-> (straightforward edge logic) c9: the 3 is forced into r1-3 and c9r4 must be white.

-> Then some extended edge logic that would be arguably deep lookahead itself:

c11: the blot forces c11r3 to be white.
This forces the 4&3 in c12&13 to be part of the 3 in r3.
Which forces the 2 in c14 to go down into r3 to finish it.
Which forces c14r4 to be white.

-> And now we have to combine the ultimate conclusion of each bit to notice that there is a space of only 4 between the two white dots in c9 and 14. That conflicts with the 6 in r4.

So r2c14-15 must be white. Then lots of line logic.


Then some summing gives us two conclusions:
Let's look at the rectangle from c1r10 to c5r13. Within it, two pixels are dotted, and there is one black pixel (part of the 3 in r13).
Horizontally, there are a *maximum* of 8 more black pixels in that space.
Vertically, there is a *minimum* of 8 more black pixels in that space.

Therefore (#1) all the horizontal clues *must* be within that rectangle and c7r9-11 must be white.
Also (#2) any vertical clues that do not have to be in that rectangle *cannot* be in that rectangle. So the 1 in c1 must be in c1r6, and the 6 in c3 must go up into r4. Then LL.


Now people who are smile logic whizzes might see that there is an uber-smile on the bottom, but as to logically.... Unfortunately, the 2s and the 3 kill true smile logic on both the bottom and the sides (without deep lookahead, that is.)

The 2s can be used, however, to find a contradiction with some extended edge logic which we could call "pseudo-smile logic". Let's choose the 2 in c1 and try it in r10-11. If it were there, c2r10-11 would be white and there would not be enough room for the 1|1 in that column. Therefore c1r10 is white.

And then the rest solves with line logic in a nice snaky fashion.


I notice that others have been voting this as "moderate lookahead". What am I missing? Can anyone tell me a better way to get started?

Okay Joe.. you're the final say but I can't understand why smile logic is used in sooo many puzzles in which it appears the same to me. Even the r2-c9 seems correctly stated by Kurt.

I didn't say that it wasn't deep look-ahead(with the 7 particularly), just that there wasn't guessing....

Tom, we've seen so many puzzles and can simply "see" some things. Sometimes we forget to count steps and many are unsure as to what exactly constitutes one step. The logic works, but I think Joe's right on the 7. It takes more than 2 steps to get there. I don't think the smile or pseudo-smile is deep though. if you start to place the 2 at the top of the 4 empty spaces available, you easily see the coming contradiction with the remaining two 1's in the c next to it. I'd imagine most seasoned solvers recognize it as a smile immediately

Kurt, thanks for replying. All I said was I agreed with your statement about r2-c9. It is true that after all these years we do gain super powers with our eyes to see the next moves. lol I am glad you SEE the smile logic as I do.

Cool solve, uncle Tom.

fun puzzle, tom!

my solve:

EL dots C1-5R1
whether C10R1 or C12R1 are black, C1-3R2 are dots
LL
whether C4R10 or C4R11 is a black, C5R10 is dot
LL to finish

thanks David, I hope the smile logic worked for you also.

no smile logic in my solve tom :)

Very good, David. This is exactly why I postponed marking this puzzle.

I looked at your "whether c10r1 or c12r1 is black" and came up with "c9r2 must be black". Which then gives line logic to the same extent as your hint. And also the same as the LL after my first (deep lookahead) hint.

(The 4 in r1 must cross c10 if placed all the way to the left or c12 if all the way to the right. It *must* cross one or both. Then the 7 in r2 must extend back into c9.)


I see my second hint that used summing is unnecessary in either of our solves, but still is cool.

Then either of our ending hints will finish it.

Found to be solvable with moderate lookahead by infrapinklizzard.

thx Joe

at some point i'll have to go back though this and follow your solve, joe. glad i could be of assistance.

No place above does anyone say what this is.

check #5 blackcat :)

yeppers

This is evidence that BlackCat reads the comments, but there's still no evidence s/he comes back to read replies.

"Niece" is misspelled, in the title. ;)

thx K

Did a lot of guessing for such a small puzzle.

Valerie: here is a puzzle that I don't own where I determined the solvability and it has since become voteable again.

Joe - Thanks for letting me know. I need to cycle back to looking at what's causing that.

Just a note that I don't see most puzzle comment threads, especially if the puzzle is bigger than 20x20. It's only luck that I saw this comment at all. The best way to reach me is with e-mail, or the e-mail form on my website. Another option is to leave a comment in the WebPBN Facebook group -- those reach me quickly too.

well if luck brings you back here some day, know that you are loved

How did your niece like the noose?
was it a nice niece noose?

David, you too are loved!

Found to be solvable with moderate lookahead by wombatilim.

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