Hashiwokakero

Hashiwokakero, also called 'Bridges', is a Nikoli puzzle in which the aim of the game is to connect all the circles (islands) by drawing lines between them (bridges). It's a straight forward puzzle, but there are some rules that need to be followed, which can increase the difficulty tremendously depending on the grid you play on. The grid can be as small or large as you like, but the difficulty often comes from figuring out how to connect islands with their neighbors, something the size of the grid doesn't affect all that much.

The rules are as follows:
- All islands must be connected in a single system, meaning you can't connect 4 islands on their own and then connect the remaining islands for example.
- The bridges must begin and end at an island, and be drawn in a straight line going either horizontally or vertically, but not diagonally.
- Bridges cannot cross islands or other bridges.
- You can have at most 2 bridges connecting the same two islands.
- The number of bridges connected to a single island must be equal to the number written on that island.

Standard version

Hashiwokakero can range from very easy to moderately difficult in terms of difficulty, but no matter the difficulty the puzzle is usually always solved easiest through a process of elimination. Figuring out which bridges must absolutely be drawn helps with figuring out what others will then have to be drawn as well.
There are other elements that could help as well though. For example, islands in corners and against the sides only have 2 or 3 paths to take, depending on the number on that island you can often tell that at least 1 bridge will have to be drawn in each direction.

Furthermore, islands with a number 7 will have at least 1 bridge in each direction. An island with the number 8 will have 2 bridges in all directions.
Bridges that would close a circuit cannot be placed, so knowing these can often reveal the only other option for that island.

Converting it to an RPG setting.

Hashiwokakero is probably one of the easier Nikoli puzzles to adapt to an RPG setting since the puzzle itself has some imagination element to it already. Connecting islands with bridges, rather than circles with lines, immediately calls upon a mental image, whatever this image may be it is a first step into converting this puzzle to an RPG setting.

In the example below my character finds herself on a pillar (instead of an actual island). All she can see are the other pillars, 4 portals, and 2 chests. She's been given the numbers and knows she can create pathways connecting the islands. However, in this version you cannot undo the creation of a path, so careful planning will be required.

Should my character fail to figure out the puzzle properly she might miss out on a portal or chest, but if she is able to figure it out she'll have access to all the portals and all the loot.
By having multiple portals I, as a game master (GM), make sure the players will always be able to reach at least 1 portal (unless they purposely do everything wrong). This means I will be able to continue the story even if it means they technically reach the wrong portal, I'll simply pretend it is the right one.

Hashiwokakero can be converted in other ways as well though. The islands could be beacons and the lines could be energy or light, connecting everything correctly will open up a door for example.
Perhaps bridges can only be traveled on once or in only one direction. So two bridges will be required to travel directly between two islands or a different route will have to be found. This does require some more planning on your side however, if the 'one way only' rule was applied to the example above players would be able to get stuck on some of the outer pillars.