Qua locus

Keeping both eyes on the long game.

Magical Hats

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Some people are on an island…

One morning, they wake up to discover that some of them have had magical hats stuck on their heads the night before. It is impossible for someone to directly sense if they have a hat on their own head, but the hats on other people’s heads are all visible to each person. Also, everyone can shut their eyes and sense if anyone is still wearing a hat. Pretty crazy, but like I said – magical hats.

The hats can only be removed by going for a swim at midnight, and the people all want to remove the hats as soon as possible. However, going for a swim if you aren’t wearing a hat is really really unpleasant and nobody trusts anybody else.

How many nights before all the hats have been removed?

Supplementary problem: How many nights before all the hats are removed if the people trust each other?

Written by CGF

June 23, 02012 at 18:37

Posted in Puzzles

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  1. Number of nights = [spoiler title=”Spoiler Alert”]number of hats. If there’s only one, that person will see no one else has a hat, so since they know SOMEONE has a hat, it must be them, and they’ll go swimming on the first night. If there’s 2 hats, each person with the hat will see 1 person with a hat, and since they didn’t go swimming on night 1, there must be 2 hats… etc[/spoiler] (though if there’s only one hat, that person may not trust anyone about the whole “magical hat” thing in the first place)

    If they trust each other, then they’d just discuss the number of hats and sort it out on the first night.

    Brian Harrington

    June 23, 02012 at 19:15

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