One of the duties of a park ranger is to protect parklands by ensuring people stay on designated trails. In these puzzles, it is your job to assemble trails of different lengths using the available paths through the forest.

Each trail must form a loop that does not overlap itself and must pass through at least one trailhead (black circle with white dot). Different trails may share paths, but all paths must be used by at least one trail. Finally, each puzzle will give specific instructions to the number of trails and their lengths.

Here is a series of paths that need to be assembled into trails. The numbers beside each path segment represent how long each segment is, in miles. In this example, the two trails created must have lengths within 1/2 mile of each other.

Here are all of the possible loops that could be made into trails for this example:

Because the orange loop does not go through a trailhead, it is not an acceptable trail.

Here are more examples of loops that are not acceptable trails: loops that overlap themselves.

Here are two acceptable solutions to the puzzle. In both cases, the trails are acceptable loops of length within 1/2 mile of each other.

Here are two unacceptable solutions using the above trails. On the left, the two trails are the same length, while the instructions specifically state that trails must be different lengths. On the right, the trails are not of lengths within 1/2 mile of each other, and not all of the paths are used.

Let's reexamine three of the trails given above.

If we tried to use any of these trails to solve the above example, we'd have a problem. Each of these leaves a T-shaped intersection of paths to be covered by the second trail. Unfortunately, no trail can cover all three of the paths that emerge from such an intersection. Thus, when thinking about what trails to use, it is important to consider not only what paths a trail does cover, but also what paths a trail does not cover.