Puzzle Description:

A guy sleeping in a white recliner with his head slumped forward. A window is in the background. Well, not really...this was made for practicing "much lookahead required" kind of puzzles. See the comments for more information.

#1: Gator (Gator) on Mar 31, 2010

This puzzle requires you to exhaust possibilities and to look ahead 2 moves in some cases. See the hints for help.

There may be multiple ways to tackle this puzzle, but this is how I did it.

Line logic lets you make one cell black and then you are stuck.

Look at column 5. The 2 clue can go in 4 different places. Look how each one of these will affect column 4. If it goes in rows 2-3, 3-4, or 4-5, it will hit either the 2 clue in row 3 or row 5. So either R3C4 or R5C4 would be black. In either one of these cases, R4C4 would be a dot. Now we have one more possible place for the 2 clue in column 5 to go which would be rows 1-2. This causes R1C4 and R2C4 to be dots. The 1 1 clues in column 4 finish out the column with R4C4 again being a dot. So we just proved that R4C4 is a dot.

Now let's look at row 1. I want to focus just on where the right 1 clue can go which is R1C3, R1C4, or R1C5. We will focus on how this affects row 2. If R1C4 is black, then R2C4 is a dot. If R1C3 is black, then so is R2C3, then looking ahead one more move, R2C4 is a dot. If R1C5 is black, then R2C5 is black, then (1 more move) R2C4 is a dot. Every case makes R2C4 a dot.

Now we can do some line logic (well, a little bit - R2C5 black, R4C5 and R5C5 dots).

Looking again at column 5, you can finish the 2 clue with R1C5 or R3C5. If R1C5 is black, R1C4 is a dot, and R3C4 would have to be black. If R3C5 is black, then so does R3C4. So both possibilities make R3C4 black.

A little more line logic.

Look at row 5. The 2 clue has three possibilities. Looking at how this affects row 4, every possibility makes R4C3 black.

The rest will solve with line logic.

I hope you enjoyed this little exercise. :)

Awesome Gator, finally a puzzle where I can use my brain a bit haha. So I think this is obviously a 'requires guessing' puzzle by webpbn's definition, but here's how I solved.

So after you exhaust the line logic (R2C2), I focused on row 5. No matter where you put that 2 clue, R4C2 has to be a dot.
As a result, R5C2 is black and R5C4/C5 are both dots.

Using the same logic as Gator, you can establish that R4C4 is also a dot. That allows you to solve out Row 4, and the rest of the puzzle nicely.

Again, this puzzle was awesome, and definitely thought provoking. I'm also liking the whole (advanced logic) preface on the title.

P.S. if you flip the image 180 degrees you kind of see an anime face crying '^_^

I purposely didn't mark this as "solvable with logic" because I wanted to see what people thought and to hear how they went about tackling this puzzle.

I tried coming up with a recognizable image, but I gave up after a while and focused on the logic.

i spolved it the same way ant did at the beginning. then i used simple "edge logic" on the 2 clue in column 5 and it was fairly easy.

i see the man in the chair, and the window, and it looks great!

thank you for the very fun puzzle.

Yeah, I don't see this as being too complicated: intermediate edge logic on the 2 in column 5 shows that rows 4 and 5 in column 5 are both white. That allows you to make R2 of C5 black, and the rest solves easily from there once intermediate edge logic shows that R1 in C5 is white as well.

Ditto Matt. Nonetheless, I felt very smart solving a difficult puzzle in about 2 minutes. I like the little puzzles. Keep 'em coming.

Found to be logically solvable by Gator.

Lol...I guess I just lucked out.

I filled in the only black square that can be placed without guessing. Then, I decided to see what would happen if I used that black square and added a black square immediately to its left (to fulfill the black 2 in row 2).

Wow...after that the entire puzzle solves in a minute with just plain logic!

...and I think the pic is amazing too!

If a puzzle is solvable by a backtracking algorithm, the by my definition it's solvable by logic and requires no guessing. But if I need a stack depth of two, or if there are more than say 4 possibles line patterns to try and keep track of, then I don't enjoy it, and feel that I'm merely "dry-running" some computer program, rather than using my logical and visual faculties.

I wasn't that satisfied with this puzzle: Like the ozymoe, I looked at the three possible combinations for row (or column) 2, and set out to try them in turn -- and hit on the correct one first time. So it turned out that ended up solving the puzzle by a combination of a lucky guess followed by trivial line-logic.

From all of the comments above, the simplest, most direct way to the solution is:

Focus on row 5 and look how this affects row 4. No matter where you place the 2 clue, R4C1 and R4C2 are dots. This lets you fill in R5C2 and then dot R5C4 and R5C5.

Focus on column 5 and look how this affects column 4. You can use simple edge logic to see that R1C5 is a dot.

The rest solves with line logic. So, I over-complicated this when I solved it the first time.

Yes, edge logic on the 2 in r5 and then the 2 in c5 is the way to go.

However, the moment I saw this puzzle, I was struck by the near symmetry of the clues. They are symmetrical along the NW-SE axis except for one 1 clue in each direction.

If you place a pixel in the spot where those clues cross, it solves correctly (and easily). This seems very intuitive, but I cannot come up with a theoretical reason.

I know Jan is interested in what is provable logically with symmetry, so maybe he can mull this over?

i did just that gator... col 5
great puzzle

That's a picture of me sitting there trying to figure out the logic! :-)

I envy those of you with really good working memories. My brain cannot hold that much information to look ahead that far to figure it out, so I had to guess. I have a hard enough time just keeping a 7-digit phone number in my head long enough to dial it. [sigh]

But I love the image and description.

Great image!

I also lucked out on my first guess, although it seemed like the best guess so maybe somehow there's some intuitive logic lurking deep within my brain? Anyway, I love the clever description. :)

Thanks Tom, Teresa, Jota, and Sallie.

This puzzle happened to be my 1000th solved.

I couldn't think of a better puzzle to break the 1000 barrier.

Thanks Mike.

Congrats on your 1000th!

I'm so happy I figured this out by myself! :) Good job to Gator for figuring out something it looked like.

Thanks Diana!

Excellently logical!

gretA

Goto next topic

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