Please ignore this question

I came across the brilliant 100 prisoners and a secret number and have a potential solution which I can't find any flaw with. Can you please let me know what I'm missing.

Solution: In a pre-planned way, prisoner 1-10 guess 10,20,30 .. 100. If they see a larger number on the envelope, they leave it face up else face down. Everytime a prisoner see a face down envelope, they guess 1 less than the previous prisoners guess. For example, if the 5th prisoner turns the envelope face down, 6th guesses 49, 7th guesses 48 and so on...

This strategy can ensure that 81 prisoners survive at the end which is higher than the proposed solution.

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    $\begingroup$ I think this should be posted as an answer to the other question... although my response to your solution is: How does any prisoner know "the previous prisoner's guess"? The 7th prisoner on walking into the room (in your example) doesn't know whether to guess 48 or 59? $\endgroup$
    – Graylocke
    Commented Feb 3, 2023 at 7:56
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    $\begingroup$ Sorry. I am new and wasn't sure of the right forum for resolving my doubt. $\endgroup$ Commented Feb 3, 2023 at 8:29
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    $\begingroup$ @Graylocke That question is "highly active" so you need a certain amount of reputation before you can post an answer to it. $\endgroup$ Commented Feb 3, 2023 at 8:35
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    $\begingroup$ I’m voting to close this question because this it is not a question ! $\endgroup$
    – Evargalo
    Commented Feb 3, 2023 at 8:59

1 Answer 1


Your answer assumes that each prisoner hears the numbers that were guessed by the previous prisoners. How else could they "guess 1 less than the previous prisoners guess". This is ruled out since the question explicitly states that "They have no other means to communicate or hear what earlier prisoners have guessed."

Without hearing what the previous guesses were, how would the 6th prisoner know on seeing the face down envelope whether he should guess 49 (5th prisoner turned it face down) or 38 (4th prisoner turned it face down), or 27, or 16, or 5.


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