One day, an eccentric billionaire who’s obsessed with puzzles decides that he needs to open a theme park based on them. After throwing money at the problem for a few years, he finally finishes. Unfortunately, the sight is so beautiful that he has a heart attack after looking at his work. Sad. Fortunately, his will is confusing, so everyone decides to make a huge contest out of it.
Every day, one person will be allowed into the Puzzle Room. There will be an envelope inside, containing a number from 1 to 1000. 100 people have been selected by difficult puzzle tests to compete for the prize. They will be allowed to create a plan beforehand. The money will be given to whoever makes it possible for the correct number to be guessed (for example, ruling out all numbers but one and leaving causes you to win) and NOT whoever actually guesses it. If the winner also guesses the number, then all the money goes to charity. If nobody guesses it, then the money goes to charity.
You are the first person to enter the room. What strategy ensures that you claim the money?
BONUS QUESTION: If you are the 99th person, what strategy ensures that you claim the money?
Note: No communication with other contestants will be allowed after the contest begins.