[You have probably heard this before, but this is one of those puzzles which seems impossible at first, and has a simple solution, not requiring anything more than 10th grade mathematics]
A mathematically minded warden with the power to release his prisoners decides to play a game with them.
He tells them:
"Tomorrow, I will assemble all 100 of you in the common room at 10AM. Prior to coming in the common room, each of you will separately in your cells have an integer between 1 and 100 (including 1 and 100), painted on your head. The numbers could repeat (e.g. all of you could have the number 27 painted on your heads).
In the common room, you will be able to see the numbers on the other 99 prisoners, but not yours. There will be no communication (direct or indirect) allowed between the prisoners.
You task is to try and guess your own number solely based on the other 99 numbers you see and no other information. Each of you will have a guard on you at all times, so if you try any funny business, it will be isolation for all of you. You will all, at exactly 10:15AM, whisper your guess into your guard's ear.
Tonight, you can discuss any strategy you like. If any single one of you is able to guess their number correctly, all 100 of you will be released.
If you guess correctly, I will require you to tell me your strategy. You will be released only if I find it mathematically valid."
What should the prisoners do?
[Solution]
A mathematically minded warden with the power to release his prisoners decides to play a game with them.
He tells them:
"Tomorrow, I will assemble all 100 of you in the common room at 10AM. Prior to coming in the common room, each of you will separately in your cells have an integer between 1 and 100 (including 1 and 100), painted on your head. The numbers could repeat (e.g. all of you could have the number 27 painted on your heads).
In the common room, you will be able to see the numbers on the other 99 prisoners, but not yours. There will be no communication (direct or indirect) allowed between the prisoners.
You task is to try and guess your own number solely based on the other 99 numbers you see and no other information. Each of you will have a guard on you at all times, so if you try any funny business, it will be isolation for all of you. You will all, at exactly 10:15AM, whisper your guess into your guard's ear.
Tonight, you can discuss any strategy you like. If any single one of you is able to guess their number correctly, all 100 of you will be released.
If you guess correctly, I will require you to tell me your strategy. You will be released only if I find it mathematically valid."
What should the prisoners do?
[Solution]
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