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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