Puzzle Description:

Nine

#1: Joe (infrapinklizzard) on Oct 2, 2018 [HINT]

Line logic gets seven black and twenty-eight white pixels.

Here is a concept to keep in mind: when 2 clues cross, it means one of two things. Either they make 2x2 blocks, or they make a zigzag.
In a confined space, the zigzag must end, and when it ends it will always have a clue that is different than 2.
Since this puzzle has only 2s, there can be no zigzags.

onward with the logic:

extended edge logic 2 r8 - if it were in c3-4 then it would make the rest of r8 white, which would force the three black pixels in r9 down into r10 causing a conflict. So r8c3 must be white.

If the left 2 in r6 were to extend into c3, then there would be no way for the two 2s in c1 to fit without conflict. So r6c3 must be white.
LL

Along the same line, if the middle 2 in r6 were to extend left into c4 then there would be no way to arrange the three 2s in c6 that would not create a conflict in c5. So r6c4 must be white.
LL

edge logic 2 c4 = r7-8 white

the three blocks of two in r5 cross 2s that must each either go up or down. (remember that they must all be in blocks of 2x2) Since only one block can go down, two must go up. And since there are only two 2s in r5, r5c3-4 can never be black (and so must be white).

====
Look at the 2 in c3. Place it anywhere you like. Notice that if the crossing 2s were to go left into c2, there would not be enough room to place the top 2 in r1 without conflict. So it must go right and make a block of 2x2 in c3-4. Using this knowledge:

If the 2x2 in c3 and c4 were in r1-2, it would force the top 2s in c1-2 and c5-6 into r3-4. So far so good, but then that would make the spaces under them in r5 white, leaving not enough room for the two 2s in that row. So r1c3-4 must be white.
LL to finish.

Found to be solvable with deep lookahead by infrapinklizzard.

That was fun!

That was hardcore. I was proud of myself for understanding that the clues could only form blocks and not zigzags, but overall, this went deeper than my own logic skills to date. This puzzle, therefore, challenged me to grow. Thank you for the walkthrough hints; they were very helpful.

(I am marking my comment as a spoiler only because I want to conceal that I had stated plainly that this puzzle has no zigzags, just blocks.)

I was able to figure out that there were 9 blocks, but I got stuck half way through. A little too deep for me. But fun for sure.

Line logic gets seven black and twenty-eight white pixels.

After that ... top left is eater black or white ... make it black and it solves until the and, make it white and it has a conflict after few steps ... so r1c1 is black.

You have to go very far ahead to find a conflict, though. I placed forty-four pixels before a conflict became apparent. That is trial and error.

To be considered logical on this site, you must be able to give a logical reason for each marking of the board before it is marked. No erasing or backtracking.

Joe, I'm not following your hint: "edge logic 2 c4 = r7-8 white"?

Here's how I solved it, only one step that I'd consider more than moderate lookahead:
LL
EL bottom 2 in C1: C1 R6 is black
IEL bottom 2 in C6: C6 R9 is black
IEL middle 2 in C6: C6 R6 is black
LL
2-way 2 in R10: R8 C3-4 is white
LL
"3-way logic" in 2 in R7: 3 possible positions: C1-2, C5-6, C8-9
For each position, the whites in the other positions will force 2x2 blacks into R5 (always satisfying the 2x2 blacks in R5, so keep looking...) in turn forcing 2x2 whites in R4.
Two of those three options contradict the 2x2 blacks in R4.
So C7 R8-9 is black.
This doesn't feel very different from deep edge logic, so deep lookahead?
LL to finish.

Philip: read it like
"Edge logic on the 2 in column 4 makes row 7 to 8 (in column 4) white."
(This is because it would make a block of four in c5.)


Your way definitely works! If I were writing the walkthrough, I would have added the not-entirely-necessary step of having the 3-way make r5c3-4 white to make the next step more obvious.
That said, yours is less lookahead than mine. In fact, its in the grey area between moderate lookahead and deep lookahead. On hard puzzles I generally lean to the deep when that happens, so I guess I will leave it as deep lookahead.

Thanks for the explanation about zigzags. That will be useful in the future.

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