5 star logic puzzle is NUTS

[Osmium]

https://steamuserimages-a.akamaihd.net/ugc/2412312108034642779/F31F62685686FD541CF17BF50330E9748CD661A2/?imw=5000&imh=5000&ima=fit&impolicy=Letterbox&imcolor=%23000000&letterbox=false
I've spent over 5 hours today on this puzzle and I think roughly 5 additional hours yesterday. It certainly lives up to its reputation as one of the hardest logic puzzles in the game. I've had to do the entire puzzle so far without hints because the game will only indicate one seemingly random square with foresight. It highlighted this one extremely early on, like it's the easiest and most logical starting point.

Go to the top left corner and then move right two and down five to reach the square marked with foresight. It's where the vertical 6 column and horizontal 5 row meet. For everything else in the puzzle I've only had to see between 1-5 moves ahead and could do it in my head. When picking the wrong color for this one, it took me a minimum of fifteen moves to reach the earliest contradiction. Is there some logic I'm missing or is the insane difficulty spike intentional?

[TNTDragons]

I think this puzzle is intentionally the hardest in the entire game. Deserves 6 stars. If it's any consolation, I shared the solution with friends when I finished it, so I can confirm that you've not made a mistake from what I can see (though I could've easily missed something)

Overall, I would advise against using the strategy of "Let's assume cell is X, and see if it leads to a contradiction". More often than not, the contradiction will come way down the line. I made a mistake at some point in the puzzle, and only reached a contradiction 30 minutes later, with dozens more cells filled in. had to re-do it from scratch essentially, only to then do a mistake later again, and having to roll with fixes "Live" (I made it a rule for myself to not use foresights). That's not to say that trying this every now and again won't be helpful, but as you correctly noticed, most puzzles in the game will only require you to look a few steps ahead, so don't go further than that.

That being said, you can try filling in the board just semi-randomly. This will give you information about which areas are more problematic than they might seem, and which are more malleable. You can then look around those areas and try and logic your way into pushing them forward a bit.

Another tip is to try and use broader strokes. Rather than "If I color this cell X then this other cell would have to be Y" try and doing more general ideas of "if I color this cell black, then this light cell has to travel through Y to connect to the rest of the grid". Admittedly you will still need to think about individual cells, but it's less about solving the puzzle and more about thinking forward to try and find the cell that has the shortest time to a contradiction.

Finally, I realize this only now, but there is a certain... "hidden rule" that might make this puzzle 10 times easier. I recommend checking the star structure underneath the southern edge of Autumn Falls or just look through your Insight Encyclopedia if you want. And if you're too lazy, then click on the spoiler -> The existence of "All light cells are connected" and "all dark cells are connected" at the same time results in a 2x2 checkerboard pattern to be impossible.

To me, this was the hardest puzzle in the entire game, so keep pushing and hopefully you'll get through it all!

[Ankhanage]

Where is this puzzles location ? I must've missed it or ignored and forgot lol

[TNTDragons]

Originally posted by Ankhanage:

Where is this puzzles location ? I must've missed it or ignored and forgot lol

At the top of the highest temple in Serene Deluge. Highest spot in the (mainland) world essentially

[Osmium]

Originally posted by TNTDragons:

Originally posted by Ankhanage:

Where is this puzzles location ? I must've missed it or ignored and forgot lol

At the top of the highest temple in Serene Deluge. Highest spot in the (mainland) world essentially

Yep. To add to this, there are two 5 star puzzles on top of that temple and this is the one on the eastern side. It's technically not at the absolute top, but it's on one of the highest ledges that has a horizontal surface to stand on. It might be possible to get up there without super jump, but I couldn't find a way.

[Ankhanage]

Ah yes I know them but really forgot about them after deciding to go for 100% Verdant Glen and Lucent Waters, will do them now. Thanks for the answers

[Vardis]

Originally posted by Osmium:

Go to the top left corner and then move right two and down five to reach the square marked with foresight. It's where the vertical 6 column and horizontal 5 row meet. For everything else in the puzzle I've only had to see between 1-5 moves ahead and could do it in my head. When picking the wrong color for this one, it took me a minimum of fifteen moves to reach the earliest contradiction. Is there some logic I'm missing or is the insane difficulty spike intentional?

I remember that one being a pain. While it's usually good, I found for this puzzle that Foresight doesn't always give you the next most reasonable deduction. That one in particular I also found weird.

The shortest way that I see to determine that a dark cell doesn't work there is that if it was dark, the cell above the 6 would have to be light. If that was light, the cell to the left of that could be dark or light, since nothing else constrains it (it's not cutting anything off, and it isn't in view of any of the viewpoint number cells.

Since the solution must be unique, the cell above the 6 has to be dark, which then forces the cell to its left to also be dark.

If you ever see a situation in these logic puzzles where you're saying "If X is true, Y doesn't matter", then X is false.

[TNTDragons]

Originally posted by Vardis:

If you ever see a situation in these logic puzzles where you're saying "If X is true, Y doesn't matter", then X is false.

This is actually something I consider as the highest level of "insight" you can have. The rule of "One and only one solution exists". It's extremely easy to mess up, and I remember I had to use it to get out of fixing a simpler mistake I made earlier. However, I don't think you need to use this rule to solve any of the puzzles, though it can make some easier (I use it all the time to speedrun puzzles in the mainland)

[Osmium]

Originally posted by TNTDragons:

Originally posted by Vardis:

If you ever see a situation in these logic puzzles where you're saying "If X is true, Y doesn't matter", then X is false.

This is actually something I consider as the highest level of "insight" you can have. The rule of "One and only one solution exists". It's extremely easy to mess up, and I remember I had to use it to get out of fixing a simpler mistake I made earlier. However, I don't think you need to use this rule to solve any of the puzzles, though it can make some easier (I use it all the time to speedrun puzzles in the mainland)

That's funny because I've noticed that elsewhere in this puzzle and in other puzzles but I consider relying on ambiguity cheating if I can't justify a block's color any other way. It's using meta knowledge, which is outside the logic of the puzzle. It's like knowing that no puzzle is unsolvable or requires a completely unreasonable leap in logic because people would have complained about it in the forums.

Maybe I'm not being consistent because there are some situations where I don't consider meta knowledge cheating. If I see a puzzle on a platform floating in the sky, I know I'm supposed to be able to reach it somehow because they wouldn't put a puzzle there otherwise. If I can get up there with some physics glitch, I'm probably not going to keep looking for the way that I was supposed to get up there.

Going back to the original point, knowing what color a block should be can make it easier to focus only on potential logical paths that will either prove it to be correct or prove the opposite to be false. I've done this before, but always need that second reason other than "this puzzle would have more than one solution otherwise and surely they wouldn't allow that". Like you said, you need to be certain about the ambiguity or this will throw you way off.

Another reason I don't rely on ambiguity is because I heard one of the galaxy puzzles has multiple solutions and figured they might do that trick more than once. I also haven't done all the mysteries yet and some of them might involve solving a puzzle both ways or something.

[TNTDragons]

Originally posted by Osmium:

Another reason I don't rely on ambiguity is because I heard one of the galaxy puzzles has multiple solutions and figured they might do that trick more than once. I also haven't done all the mysteries yet and some of them might involve solving a puzzle both ways or something.

It's not that it has multiple solutions, it's just that the puzzle is an environmental one that can be solved in two different ways (both of which will reach the same solution). There are a few puzzles like this, especially in the pattern boxes

As a side tangent, I've been doing some thinking and I think you might be able to use mathematical analysis to prove that you never need to use this meta approach to a puzzle. Explanation below might be a bit hand wavy, but in general if only one solution exists under the rules of the puzzle, then if X causes Y to be ambiguous, that means X has to also break some rule somewhere within its sphere of influence. So while X causes Y to be ambiguous, it will also cause Z to be a contradiction. This means that the meta analysis is just the other side of a coin for "Assume X, see if it creates a contradiction" method that is a very common way of finding where and how the rules might be broken. It's just sometimes it's faster to find it cause an ambiguity than a contradiction, but also it's much easier to be deceived into thinking of something as ambiguous when it's actually not

[wervyn]

Ah yeah, I remember doing this one, it was fun. To provide some actual hints on how to make progress on this puzzle, I can see a couple of obvious things right off the top of my head using the checkerboard lemma. Look at the unfinished 5 near the left edge (r11c19) and the squares immediately below and to the left; both of those need to be black, or you'd end up with a checkerboard pattern, which will eventually lead to violating the all white/black must be connected rules. Now look a little above that to find another instance at r4c17, which has to be painted white. That allows you to complete that 5, and then the 7, and then the original 5, which should give you a lot more to work with.

The checkerboard lemma is a really useful trick that you should always be on the lookout for in puzzles that have a paired white/black connection rule. It's something I'd never really considered until this game pointed it out, even though it's pretty easy to prove to yourself once you think about it. I've used a similar trick for a long time for any puzzle involving Nurikabe rules where just the black cells need to be connected, noting that you can never make a fully white chain (including diagonals) that touches the edge in two separate places, which is something this game doesn't explicitly call out as an insight. Realizing that there was a completely local rule that you can apply when both connections need to be maintained was really cool, though.

[TNTDragons]

Originally posted by wervyn:

noting that you can never make a fully white chain (including diagonals) that touches the edge in two separate places, which is something this game doesn't explicitly call out as an insight.

Pretty sure this is an insight, though it's more general and applied to "all blacks/lights connected". It says that if that is the case, you can only have one continuous stretch of a single color across the border, meaning you can't go black-white-black-white for instance. Not quite what you were saying, but I think it's the same general intuition

[wervyn]

Originally posted by TNTDragons:

Pretty sure this is an insight, though it's more general and applied to "all blacks/lights connected". It says that if that is the case, you can only have one continuous stretch of a single color across the border, meaning you can't go black-white-black-white for instance. Not quite what you were saying, but I think it's the same general intuition

That's correct, the border rule is a consequence of the same insight applied to both colors. It's just a more general rule that can be applied when only one of them needs to be connected.

[Toack]

This was my favorite puzzle in the game, no hidden outside rules (like prime numbers) or some bizarre bizarre reasoning that will lead you to a contradiction 20 moves after or time consuming (no more than what the size of the board deserves). I wish all puzzles were like this.

[TNTDragons]

Originally posted by Toack:

This was my favorite puzzle in the game [...] I wish all puzzles were like this.

Small suggestion: To the north-east of the Lucent Waters Fast Travel, there is a path that leads to an Enclave (Shattered Library I think). On the way to that enclave there will always be 3 puzzle boxes, whose difficulty ranges from 5 to 10. (5 orbs to 5 stars) but usually is around 6-7. It's not as great or time-consuming as this puzzle, or the one at the southern tip of Autumn Falls; but they refresh every day AND are different on every server, unlike every other puzzle in the game. That means that quite frequently whenever you log into a game, there will be some fresh puzzle there.

Additionally, when solved once these puzzles stay solved, meaning that you won't be suckered into re-solving puzzles you've done before, like with every other refreshing puzzle

[Toack]

Nice spot! I

Originally posted by TNTDragons:

Originally posted by Toack:

This was my favorite puzzle in the game [...] I wish all puzzles were like this.

Small suggestion: To the north-east of the Lucent Waters [...] like with every other refreshing puzzle

Nice spot! I missed it completely, although i couldn't find the one at the southern tip of Autumn Falls... care to share a screenshot ?