Slitherlink

Slitherlink, sometimes called 'Fences', 'Takegaki, 'Loopy', and a few other names, is a Nikoli puzzle in which the aim of the game is to connect dots/corners of cells on a grid so they form a single loop. The game can be played on any grid size, but the larger the grid the more difficult the puzzle often becomes. The difficulty of a Slitherlink puzzle does depend more on the number hints and the overall shape of the solution however.
Slitherlink's also traditionally played on a grid with square tiles, but other tiles work as well.

The rules are as follows:
- Connect the dots/corners next to the numbers in the grid so that they form a single connected loop.
- Dots/corners can only connect vertically and horizontally.
- The numbers indicate how many line segments have to be around that number.
- The loop has to be as small as possible, so detours and other unnecessary lines are not allowed.
- The loop cannot branch off or cross itself.

Standard version

Solving a Slitherlink puzzle can be a little daunting at first sight, but once you know the rules and the overall way the puzzle works it becomes easy enough to solve.
The best places to start are number clusters, especially a 3 and a 0 together. If a 3 and a 0 are together you know all the lines around the 3 need to be drawn, with the exception of the one in between the 3 and the 0.

There are many deductions you can make based on number pairs, positions of certain numbers, available lines, and so on. Since it does rely heavily on deductions, this puzzle isn't always ideal for the less puzzle enthusiastic RPG groups, but it can definitely offer some fun adaptations.

Converting it to an RPG setting.

Uncovering a secret route, connecting a flow of energy, hiding the path of a ley line circuit, showing the route somebody took through a city. These are just a few of the adaptations you can create using Slitherlink as a basis.

In my example I went with a 'safe path' adaptation. My character finds herself on a path (orange line) that leads her into a dark cavern. Earlier she was given the numbers as a clue, as well as the information on how to solve a Slitherlink puzzle.

As long as she sticks to the path the solution of this puzzle would give her she'll be fine, but if she ever wanders off the path she'll find out the floor isn't actually solid all across the room, only on the safe path.
Once she makes it to the other side she'll be able to continue onward. The route she takes (left or right) won't matter, but you could add different monsters, loot, and anything else you might wish to throw at people.

Creating a Slitherlink puzzle can be tricky. The biggest difficulty lies in giving just enough number hints to make it challenging enough. Give too many and the puzzle becomes too easy, give too few and the puzzle becomes either impossible or ends up having multiple solutions.