Cheating on a string theory examAnd now for something completely different: I've been enjoying FiveThirtyEight's "The Riddler" puzzles. A couple weeks ago I submitted a puzzle of my own; but I haven't heard back and it's too cute a puzzle to not share, so I've decided to post it here.
You have to take a 90-minute string theory exam consisting of 23 true-false questions, but unfortunately you know absolutely nothing about the subject. You have a friend who will be writing the exam at the same time as you, is able to answer all of the questions in a fraction of the allotted time, and is willing to help you cheat — but the proctors are alert and will throw you out if they suspect him of communicating any information to you.
You and your friend have watches which are synchronized to the second, and the proctors are used to him often finishing exams quickly and won't be suspicious if he leaves early. What is the largest value N such that you can guarantee that you answer at least N out of the 23 questions correctly?
Extra credit: Explain the connection between your solution and the topic of the exam.
For clarity: No, you cannot communicate information based on which hand your ambidexterous friend uses to write his exam answers, based on how quickly he walks on his way out of the exam, or any other channels not stated: The proctors will catch you and you'll get a zero on the exam. The only information you can receive is a single value: When your friend left the exam.