Find the safe path through the dungeon!

Question

You need to get from the bottom to the top.

But this dungeon puzzle is extremely ancient, and unfortunately, the symbols on the tiles are no longer visible. Stepping on an unsafe tile means certain death.

However, you can clearly see there are dead bodies/remains on certain tiles (represented by skull & bones).

You also know the following:

1. There is exactly one safe path through the dungeon.
2. You cannot move diagonally.
3. The path does not double back on itself (a safe tile is directly adjacent to at most two other safe tiles).

For clarification, there is no distinction between dotted and solid lines. A "tile" is simply any square within the boundaries. Each skull is inside exactly 1 square tile. (This puzzle is for a game of Dungeons and Dragons I'm hosting soon, and I want to make sure the puzzle isn't too hard/easy and is logically consistent).

Answer 1

I'll have to add a full proof later, but here's the gist:

Some key points:

Each skull is not only an indicator of a death square, but also an implication that the path is adjacent, otherwise the poor soul would not have been able to reach that square.

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We can't have dead ends. Otherwise, the path doubles back on itself.

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Only one cell of the path can be adjacent to the start line at the bottom, and likewise for the end line at the top.

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Square D8 (take a guess) is important because the skull to the right is only reachable from this square. At the other two open squares, the path would get trapped, and there will be a dead end.

( If you've been writing an answer for an hour, go finish it because it's probably better than this lol)

Answer 2

This answer is going to be more focused on the last part of the question. I'm not drawing a solution out as greenturtle has already done so with, I believe, the correct answer.

So you're going to be using this for a DnD session and you're worried about inconsistency; it looks like all the criteria you have laid out are met, the only issue I am seeing is in regards to the starting and ending squares. Depending on how you as the DM interpret the singular path there could be some issues. For example, greenturtle's solution has you staying on N2 (bottom row second column) but theoretically the path could start at N5 and go over to N2 before following the path that greenturtle laid out. This would be pointless because there is no value in having a safe set of rules that run parallel touching the safe zone, but it could happen then if you entered at N2 you would be following the same singular path just not following it in its entirety. Then as the DM you would have to rule of that is valid or not or of by starting on an otherwise safe space out of order it invalidates the safety of the space. While I do think the intent was to have the single solution be the one shown by greenturtle this might be a role with clarifying and stating to the players 'only one safe tile makes contract with the entrance' or some such, just because you will be amazed with the sort of odd ball solutions PCs will come up with. Same issue applies with the exit, can be handled the same way just with noting that it could be an issue.

Lastly I'll just say that you might want to keep handy clues in mind for if they do get stuck, because nothing kills a session like getting stick on a puzzle that you just can't solve. As I'm sure you know, though it wasn't written out in the question, one of the unspoken rules of the puzzle is that all crossbones are adjacent to a safe tile. This sorry of hunt didn't completely give away the solution but makes it substantially easier and might be good to have on hand as a hint of they get stuck and can make a dungeoneering check, or maybe survival if you're playing 5E.

Anyways just wanted to approach this from a more D&D focussed point of view because the game has a way of bringing up small little issues you never would normally expect to run into. Was going to make this a comment but it got a bit lengthy .....