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Microsoft Interview Question for Software Engineer/Developer about Puzzle
(6 posts)-
A bunch of men are on an island. A genie comes down and gathers everyone together and places a magical hat on some people’s heads (i.e., at least one person has a hat). The hat is magical: it can be seen by other people, but not by the wearer of the hat himself. To
remove the hat, those (and only those who have a hat) must dunk themselves underwater at exactly midnight. If there are n people and c hats, how long does it take the men to remove the hats? The men cannot tell each other (in any way) that they have a hat.FOLLOW UP Prove that your solution is correct.
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After C days.
Consider a person A wearing the hat.
A shall see C-1 hats.
If A thinks he is not wearing the hat, then he would expect the others to realize that they are wearing a hat in C-1 days, and have a dunk after C-1 days.
But since they did not, that means A is also wearing a hat, so they shall dunk in C days.Move C from 1,2, 3... to verify the solution.
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I think this question is incomplete but still... lets answer
1)
As no one can tell other that he has a hat, but will see C-1 hats around.
And only those can dunk who are having hat, but there is no way to know for a person that he has hat.
hence it's a dead lock....2)
If all are known that there are C hats, the person having hat can see C-1 hats then it's easy to infer he is having a hat and will dunk at first midnight
similarly all can know before the first midnight....
Hence only one midnight is required to remove all hats -
2*C
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Sonam can you explain
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Manik has the right answer already. C+1 days or as he said, after C days. This question has many varieties ranging from evil imp releasing the dwarf to unfaithful husbands in a village.
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