Confused by late game black and white

[Showd]

I don't understand late game black and white puzzles, like the one outside the gallery. I'm stumped. What's the rule exactly?

[xicmiah]

I also would appreciate some help.
Here's my intuitive understanding, it's probably wrong but it worked for the ones above the gallery:

First, white and black blocks stand for same colors in solution.
Next, about absent blocks. Divide the sculpture into blob-like areas, also colored "white" and "black"; "white" area can contain only white blocks, "black" area can only contain black blocks, empty spaces in sculpture can be in either.
Now, fill empty spaces from the sculpture based on area they are in: empty space in "white" area means black square in solution, empty space in "black" area means white square in solution. This should fill the rest of the solution.

[Samantha Prezombie]

Originally posted by xicmiah:

I also would appreciate some help.
Here's my intuitive understanding, it's probably wrong but it worked for the ones above the gallery:

First, white and black blocks stand for same colors in solution.
Next, about absent blocks. Divide the sculpture into blob-like areas, also colored "white" and "black"; "white" area can contain only white blocks, "black" area can only contain black blocks, empty spaces in sculpture can be in either.
Now, fill empty spaces from the sculpture based on area they are in: empty space in "white" area means black square in solution, empty space in "black" area means white square in solution. This should fill the rest of the solution.

The problem with this logic is the solution for the bottom right block puzzle above the house. 7 tiles, 4 unknown, you need to "cut" the blank area into 1 tile spaces.
It really feels like they dropped the ball with those block puzzles, since the rest of the tutorial had the blocks reflected in the larger world, but the 7 outside the tutorial don't have any clear companion clues, which feels like both a waste of a good set of puzzles, and would've been far more helpful for teaching about The Big Secret.

[HikariStarshine]

The logic rule I worked with was 'If a blank space has 2 of one color adjacent to it, color opposite'. Seemed to work well enough.

[Samantha Prezombie]

Originally posted by HikariStarshine:

The logic rule I worked with was 'If a blank space has 2 of one color adjacent to it, color opposite'. Seemed to work well enough.

That isn't the rule either though, look at the top right, 3x5 puzzle. second and fifth row is black blank white, but the blanks are opposite colors!

[xicmiah]

Originally posted by Prezombie:

That isn't the rule either though, look at the top right, 3x5 puzzle. second and fifth row is black blank white, but the blanks are opposite colors!

I also agree with "take dominant color, color opposite of that" rule. Here's how I tried that 3x5 puzzle, row 1 is the topmost one.

1. Row 4 has 2 adjacent black, color white
   
2. Row 3 has 2 adjacent white, color black
   
3. Row 5 has adjacent 1 black 2 white (other white from row 4), color black
   
4. Row 2 has adjacent 2 black 1 white (other black from row 3), color white
   
5. Row 1 has adjacent 1 black 2 white, color black

This gives a valid solution.

100
011
101
010
001

There's probably a simpler underlying rule, but this procedure does give a valid solution for every such puzzle, including the hardest one in the secret area.

[Samantha Prezombie]

Originally posted by xicmiah:

Originally posted by Prezombie:

That isn't the rule either though, look at the top right, 3x5 puzzle. second and fifth row is black blank white, but the blanks are opposite colors!

I also agree with "take dominant color, color opposite of that" rule. Here's how I tried that 3x5 puzzle, row 1 is the topmost one.

1. Row 4 has 2 adjacent black, color white
   
2. Row 3 has 2 adjacent white, color black
   
3. Row 5 has adjacent 1 black 2 white (other white from row 4), color black
   
4. Row 2 has adjacent 2 black 1 white (other black from row 3), color white
   
5. Row 1 has adjacent 1 black 2 white, color black

This gives a valid solution.

100
011
101
010
001

There's probably a simpler underlying rule, but this procedure does give a valid solution for every such puzzle, including the hardest one in the secret area.

That logic does seem to work, but yeah, it feels extremely unsatisfying that the very first mechanic has no clear onboarding, along with how the tutorial gives a huge red herring on how to solve the later puzzles of this type...

[Jack]

Originally posted by xicmiah:

Originally posted by Prezombie:

That isn't the rule either though, look at the top right, 3x5 puzzle. second and fifth row is black blank white, but the blanks are opposite colors!

I also agree with "take dominant color, color opposite of that" rule. Here's how I tried that 3x5 puzzle, row 1 is the topmost one.

1. Row 4 has 2 adjacent black, color white
   
2. Row 3 has 2 adjacent white, color black
   
3. Row 5 has adjacent 1 black 2 white (other white from row 4), color black
   
4. Row 2 has adjacent 2 black 1 white (other black from row 3), color white
   
5. Row 1 has adjacent 1 black 2 white, color black

This gives a valid solution.

100
011
101
010
001

There's probably a simpler underlying rule, but this procedure does give a valid solution for every such puzzle, including the hardest one in the secret area.

As far as I can tell, this is disproved by the puzzle in front of the gallery, where following this method could lead to an accepted solution but could also lead to an unaccepted solution. For example, after doing the corners, you can mark the 2nd and 4th tiles in the middle column as black (each has two adjacent white tiles and only one black). From there, you can color the middle tile white (since it now has two adjacent black tiles and no adjacent whites). Leave the last two tiles black, since there's a tie in both cases.

I suppose it could just be an oversight that the game rejects this solution though.

(Edited to say "column" instead of "row"...kind of important!)

[ut]

i just treat it as whites are white, blacks are black, and if there are blacks that have a void space between them i color it white. a row that looks like B - B would become 0 1 0, and B - - B would become 0 1 1 0. maybe thats not the right logic but its how i got through them all.

[Mattthew]

I really wish a developer would respond with the intended rule because it frustrated me this whole time as well

[taggedjc]

From what I can tell, the rule is:

All white or black blocks make the corresponding tile on or off respectively. Then, if an undetermined tile is adjacent to more on tiles than off tiles it's set off, and if it's adjacent to more off tiles than on tiles it's set on. If they're adjacent to one of each or two of each, you can choose to either make them on or off.

I'm not sure if there's a counterexample to this method.

[Curious Duck]

So at the very start of the game you encounter black and white tiles. White tiles taking up positive space and then black tiles taking up negative space

So the puzzles outside of the area for that mechanic (by the mill etc) mean you have to fit the shape that's to the side of the panel into the panel screen. Meaning you also have to put in extra tiles to create that negative space for the black tiles

[choongmyoung]

To be short:
1. Blacks are black, whites are white,
2. Maximize the number of borders between black and white.

[Jack]

Originally posted by choongmyoung:

To be short:
1. Blacks are black, whites are white,
2. Maximize the number of borders between black and white.

Nice, this is the first way I've seen it stated that seems to fully work for all the puzzles.

[Aris]

Originally posted by choongmyoung:

To be short:
1. Blacks are black, whites are white,
2. Maximize the number of borders between black and white.

I like this one, it explains all solutions while keeping it simple.

But I've found a solution that should be accepted but isn't.


A valid solution for the one in the mansion is

OXOOX
XXXOO
XOXOX
OOXXX
XOOXO

And another valid solution is the same but with the middle tile white. Given your explanation it makes sense.

But then the game doesn't accept this one (inverting the 3rd tile of the 4th row):

OXOOX
XXXOO
XOXOX
OOOXX
XOOXO

The number of borders between black and white tiles remains the same. This solution just moves the border.

[Jack]

Originally posted by Aris:

Originally posted by choongmyoung:

To be short:
1. Blacks are black, whites are white,
2. Maximize the number of borders between black and white.

I like this one, it explains all solutions while keeping it simple.

But I've found a solution that should be accepted but isn't.


A valid solution for the one in the mansion is

OXOOX
XXXOO
XOXOX
OOXXX
XOOXO

And another valid solution is the same but with the middle tile white. Given your explanation it makes sense.

But then the game doesn't accept this one (inverting the 3rd tile of the 4th row):

OXOOX
XXXOO
XOXOX
OOOXX
XOOXO

The number of borders between black and white tiles remains the same. This solution just moves the border.

Ah, true. I missed that. Also worth pointing out that an overall "maximization problem" type of rule would be a huge outlier among the other puzzle rules in the game, which can all be evaluated individually on a smaller scale (individual tiles or contiguous groups of tiles) as satisfied or not.