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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.

The Will:

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.

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    $\begingroup$ does everyone guess before they come into the room and I guess see the answer or something? Do the other contestant hear the guess? Do they at least know "someone guessed wrong"? Do they continue to enter the room after a successful guess, or does it all end at that point? Do the contestants handle the envelope alone? Does an attendant come into the room and "reset" it so that communicating through envelope positioning etc is not possible? $\endgroup$
    – Kate Gregory
    May 23 at 16:05
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    $\begingroup$ What's the motivation for cooperation? If only 1 person gets the money, why would they conspire to create a plan beforehand? If multiple people are required to guarantee the number is guessable (via a chain of guesses for instance), do they all receive the money? What happens when they enter the room? Can they look in the envelope, make multiple guesses, etc? Feels too incomplete to answer so far. $\endgroup$
    – JGibbers
    May 23 at 16:14
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    $\begingroup$ Closing until OP is able to give a lot more clarity about what the actual rules are; at present I don't think it's possible to know whether any given thing is a solution or not. $\endgroup$
    – Gareth McCaughan ♦
    May 23 at 16:33
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    $\begingroup$ I'm afraid OP may have forgotten to include the actual puzzle amid all the fancy decoration. That, or they didn't know that intended "gotcha" questions should be tagged with the lateral-thinking tag. $\endgroup$
    – Bass
    May 23 at 17:51
  • $\begingroup$ In what way is any information about the number released to the players? There could be nothing in the envelope, and with the current formulation of the puzzle, none of them would ever get to find out. $\endgroup$
    – Jaap Scherphuis
    May 23 at 18:41

1 Answer 1

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Despite the fact that the game is woefully ill-defined in the question body, it is clear that it is

impossible

to ensure that you claim the money.

No matter what your strategy is, it's possible that you guess the correct number on your very first try, in which case you don't get anything. It's not even possible to ensure that any of the contestants get the money - the only way to ensure that you don't guess the number "by accident" is to not guess anything at all, but if everyone does that the money goes to charity anyway.

If you're the 99th person,

It's still impossible to guarantee a win, since there is always a possibility that you pick the number in the envelope. The only way you can guarantee that you avoid it is by knowing what that number is, but if you know that, the previous person already won.

If we go with lateral thinking, you can win by

changing your name to "Charity", entering the room on the first day, and consecutively guessing all the numbers. You're guaranteed to guess the number, at which point the money goes to Charity - you.

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  • $\begingroup$ Good lateral thinking answer! I probably wouldn’t have thought of this if it were another persons question. $\endgroup$
    – Box Enthusiast
    Jun 6 at 14:58

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