You and other party-goers are lead to different places in a wood blind-folded. You’re instructed to remove your blindfold at the sound of a horn and read a letter you’ve been provided. When the bell sounds, you remove the blindfold and the letter reads thus:
You’ll notice around you that there are lengths of rope tied between hundreds of trees around you. You may notice that any tree with any rope tied to it has exactly two ends tied to it, each stretching to a different tree. In fact, these hundreds of treees form a giant concave polygon. Some of you are inside that polyon and others are outside. To win the game, you must be the first to reach the clubhouse at the top of the hill (which is outside of the polygon!) and report correctly whether you were initially inside the polygon or outside of it. You can pass under the ropes, but please don’t change them in any way. Good luck!
What strategy might you employ to determine your status and require as little time as possible to get back to the clubhouse?