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Puzzle: Wise Men

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A sultan has captured 50 wise men. He has a glass currently standing bottom down. Every minute he calls one of the wise men who can choose either to turn it over (set it upside down or bottom down) or do nothing. The wise men will be called randomly, possibly an infinite number of times. When someone called to the sultan correctly states if all wise men have already been to the sultan at least once, everyone goes free. But if his statement is wrong, the sultan puts everyone to death. The wise men are allowed to communicate only once among them and then are imprisoned in separate rooms. Design a strategy that allows the wise men to go free.

Wise Men

Wise Men

Solution: 

We should note that it is not necessary for anyone to give the answer outright. That is perfectly possible for a sage to be called and him to remain silent. The wise men’s strategy to live could be: 

Step 1: The wise men will mutually decide a leader among them. Only this person is allowed to tell if all the wise men were called.  

Choose a leader among the wise men

Choose a leader among the wise men

Step 2: When presented to the sultan, the leader among the wise men will turn the glass over if and only if he finds the glass bottom up. 

Leader flips the glass when it is bottom up

Leader flips the glass when it is bottom up

Step 3: Leader will also keep count of how many times he has flipped the glass. As for the other wise men, they will flip the glass only when they find it in a bottom-down position the first time and leave it untouched otherwise.

Wise men flip the glass when it is bottom down

Wise men flip the glass when it is bottom down

Step 4: When the leader flipped the glass 49 times, he can say with certainty that all the other wise men were called at least once. He can declare the same, and all the wise men could live.

Leader answers if all have flipped glass once

Leader answers if all have flipped glass once


Last Updated : 18 Jan, 2023
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