Suraromu

Suraromu is a Nikoli puzzle in which the aim is to create a continuous loop on a grid, while making sure the loop passes through each gate in a specific order.

The rules are as follows:
- Create a single, continuous loop on the grid, which cannot intersect itself.
- The loop has to go through each "gate", and can only go through them once. A gate is a dashed line. If two dashed lines are next to each other, and thus form a continuous line, they still count as one gate.
- The loop must start and end at the circle with a number. The number indicates how many gates you have to pass. Since you have to pass all gates anyway, this number is a little redundant.
- Numbers on the black squares indicate the order of when this gate is passed. The direction doesn't matter. So a 2 on a black square could mean the loop passes this gate second in either a clockwise or counter clockwise direction.

Standard version

Solving a Suraromu puzzle is usually very simple. There's often only two or three possible starts you can make, and taking one will quickly lead to a right or wrong solution. The puzzle does become slightly more difficult on a bigger grid, but even then it can be solved with simple deduction.

Converting it to an RPG setting.

Suraromu has a bunch of fun adaptation possibilities. The most obvious is to turn the dashed line gates into actual gates, perhaps in the form of a map, or in the form of a type of wild goose chase the characters might have to venture on. Perhaps figuring out the loop means figuring out the path a specific character took, and thus where that character was at specific, plot relevant times. Or perhaps it gives the characters themselves the locations of where they have to be on specific dates.

In my example below, my character is faced with a map with gates, each belonging to a town in a mountainous area. Many towns guard a path between two mountains, and are often the only way through, but my character's goal is not to pass the mountains, but to complete the trial of the mountains.
She has to be at specific towns on specific days, sometimes for a test, sometimes to gather a specific item, or witness a specific event, but always something she'll only have one chance to get right. If she picks the wrong order, she won't be able to get each stage right, and therefore fail the overall trial of the mountains.

If my character succeeds the trial of the mountains, new wisdoms will be bestowed upon her by the mountain sages, and perhaps new allies will be made. Plus, the trial of the mountains itself offers plenty of opportunities for personal growth and experience.

But there's more fun to be had than just gates and dates, the gates could instead be used to direct the flow of water or magic, so each area has a steady flow of whichever resource you picked.
Perhaps the loop is actually the only safe path, deviating from it will lead to certain doom. Or maybe it shows a route a specific character will take in the future, and by figuring it out, you can set a trap well in advance.

There's far more that could be done, from power sources to event timelines, and from patrol routes to ideal army marching paths. Order is often a crucial part however, but that alone can make for intriguing ways to give some story in a puzzle.