Puzzles with multiple solutions

[Gex]

I'm struggling with this puzzle and similar to this:
https://steamcommunity.com/profiles/76561198038235249/screenshot/2497878693362861380/

I understand how the "underclued grid" rule works, the problem is I believe this puzzle has multiple solutions. What I mean is that the marking "only what is definitely true" 27 times as requested in this puzzle is not possible with 100% certainty; since there are multiple steps with which you could succesfully solve the puzzle while respecting the conditions.

[Jet Uppercut]

You don't have to solve the entire puzzle, you just have to complete the black and white trails.

[Veralis]

It is a little confusing, but with practice you start getting the hang of it. You might have to use the hint system to work out if you've gone wrong.

In that image there's 16/27 you can fill in instantly.

Then I tend to try path of least resistance (smallest number of squares filled) with additional rules to see if that works, which brings that image to 27/27.

The right-most black squares in that image have a gap between them in the NE corner that doesn't need to be filled in.

[Gex]

Originally posted by Veralis:

It is a little confusing, but with practice you start getting the hang of it. You might have to use the hint system to work out if you've gone wrong.

In that image there's 16/27 you can fill in instantly.

Then I tend to try path of least resistance (smallest number of squares filled) with additional rules to see if that works, which brings that image to 27/27.

The right-most black squares in that image have a gap between them in the NE corner that doesn't need to be filled in.

I completed the puzzle, it's not that hard. I'm still not convinced about what the game considers steps that are "definitely true". I know the first 16 steps are obvious and those should definitely count as unavoidable, but I don't think the following ones to get to the 27 required can be considered unavoidable. I do agree that maybe they are the ones of "least resistance" like you said, so that's a good strategy.

[󠀡󠀡]

Originally posted by Gex:

Originally posted by Veralis:

It is a little confusing, but with practice you start getting the hang of it. You might have to use the hint system to work out if you've gone wrong.

In that image there's 16/27 you can fill in instantly.

Then I tend to try path of least resistance (smallest number of squares filled) with additional rules to see if that works, which brings that image to 27/27.

The right-most black squares in that image have a gap between them in the NE corner that doesn't need to be filled in.

I completed the puzzle, it's not that hard. I'm still not convinced about what the game considers steps that are "definitely true". I know the first 16 steps are obvious and those should definitely count as unavoidable, but I don't think the following ones to get to the 27 required can be considered unavoidable. I do agree that maybe they are the ones of "least resistance" like you said, so that's a good strategy.

The puzzle is trying to teach you that if you have to connect all light AND all dark squares, then there can't be any cuts. That's why they have you fill in the corners. If you still don't understand, play around with it a bit. Introduce a cut and then try to link them all up. You won't be able to.

[joridiculous]

Originally posted by Veralis:

It is a little confusing, but with practice you start getting the hang of it. You might have to use the hint system to work out if you've gone wrong.

In that image there's 16/27 you can fill in instantly.

Then I tend to try path of least resistance (smallest number of squares filled) with additional rules to see if that works, which brings that image to 27/27.

The right-most black squares in that image have a gap between them in the NE corner that doesn't need to be filled in.

Funny part with this, the hints dont work at all. All it do is show where to put a colour then next hints says its the wrong colour and this repeats for ever

Apart from that, i dont get this one at all.

[Gex]

Also it's not true that you can't have any cuts; you can have cuts and connect the area through another tile

[󠀡󠀡]

Originally posted by Gex:

Also it's not true that you can't have any cuts; you can have cuts and connect the area through another tile

If you have a cut then there will be a string of squares that can't connect. It will be one color surrounding another with no way out. Like I said, play around with it and verify it for yourself.

[ValyriaWrex]

Put a white square where the question mark is and make a path that connects to the five white dots above it -- any way you do it, you're going to cut off the two black squares that I marked with an X from the rest of the black squares: https://i.ibb.co/3hXvF9F/puzzlehint.jpg

Expanded for clarity:

The point of the underclued puzzles is to think about whether putting a square of a certain color in a certain position will make it impossible to complete.

So for example, try putting a white square where the question mark is and make a path that connects to the five white dots above it -- any way you do it, you're going to cut off the two black squares that I marked with an X from the rest of the black squares: https://i.ibb.co/3hXvF9F/puzzlehint.jpg

Since putting a white square in the "question mark spot" makes it so you can't solve the puzzle, it has to be a black square, so you should mark it as a black square in the underclued puzzle.

[Vardis]

You can't form a checkered 2x2 pattern when you have to connect both all light and all dark squares. That's one of the things that this type of puzzle is trying to teach you.

[joridiculous]

Originally posted by ValyriaWrex:

Put a white square where the question mark is and make a path that connects to the five white dots above it -- any way you do it, you're going to cut off the two black squares that I marked with an X from the rest of the black squares: https://i.ibb.co/3hXvF9F/puzzlehint.jpg

That doesn't work. No matter how i place any whites nothing happens with solution only complaints about the two back not connected. Even following all the dotted whites and blacks in the picture.
This puzzle doesn't make sense what so ever

[󠀡󠀡]

Originally posted by joridiculous:

Originally posted by ValyriaWrex:

Put a white square where the question mark is and make a path that connects to the five white dots above it -- any way you do it, you're going to cut off the two black squares that I marked with an X from the rest of the black squares: https://i.ibb.co/3hXvF9F/puzzlehint.jpg

That doesn't work. No matter how i place any whites nothing happens with solution only complaints about the two back not connected. Even following all the dotted whites and blacks in the picture.
This puzzle doesn't make sense what so ever

That's the point. The question mark tile *has* to be black or the two black pieces won't be able to link up.

[joridiculous]

Originally posted by quaixor:

Originally posted by joridiculous:

That doesn't work. No matter how i place any whites nothing happens with solution only complaints about the two back not connected. Even following all the dotted whites and blacks in the picture.
This puzzle doesn't make sense what so ever

That's the point. The question mark tile *has* to be black or the two black pieces won't be able to link up.

that is the opposite if what "valria" wrote.
I cant stand the "underclued grid" puzzles. They don't make sense. Its so stupid, you get 3 exactly the same layout and they have to be solved in 3 different ways.

[ValyriaWrex]

I edited that my original post to hopefully make the intent clearer. It's been a while since my teaching years :)

[crazy-4-finger]

There is also an Insight in the game which teaches this exact pattern. Its called
The 'checkerboard' lemma.

I knew this pattern before form different sudoku types so I used it instantly but remember it coming up pretty late in the game as an insight Which was weird since its definetely not easy to see/come up with it on your own.

[Salbris]

Originally posted by joridiculous:

Originally posted by quaixor:

That's the point. The question mark tile *has* to be black or the two black pieces won't be able to link up.

that is the opposite if what "valria" wrote.
I cant stand the "underclued grid" puzzles. They don't make sense. Its so stupid, you get 3 exactly the same layout and they have to be solved in 3 different ways.

They seem to have edited their post but it all makes sense to me. You are asked to only place tiles that are absolutely required and nothing more. That one black spot is absolutely required since without it the two block tiles would be cut off.

The point is to think about all the possibilities and reduce them to the guaranteed patterns. It's not really solved in 3 different ways. It generally follows the same strategies of regular logic grids except that when there is ambiguity you just don't place the tile. I haven't seen advanced ones like this yet but I wouldn't be surprised if you would have to "solve" the entire grid sometimes and then delete tiles that are ambiguous.