In a spooky video game, you are dropped into the middle of a haunted maze. The maze has only one exit. There are three paths at every intersection: the one you are coming from, one that goes left, and one that goes right. Show that this maze must contain a cycle (that is, there is some place in the maze where some sequence of choices to go left or right will lead back to the same place).

In a spooky video game, you are dropped into the middle of a haunted maze. The maze has only one exit. There are three paths at every intersection: the one you are coming from, one that goes left, and one that goes right. Show that this maze must contain a cycle (that is, there is some place in the maze where some sequence of choices to go left or right will lead back to the same place).