Discuss Try this Puzzle within the DI / DS forums, part of the CAT, XAT, MAT, CET, JMET and other Indian MBA Entrance Exams category; There are ten gnomes. They are in the dungeon. Their captor has given the gnomes a chance of survival. Here ...
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Try this Puzzle
Try this Puzzle - March 7th, 2008
There are ten gnomes. They are in the dungeon. Their captor has given the gnomes a chance of survival. Here is the offer:
He lines the gnomes up in a single-file row. This means that the tenth gnome sees the back of the person in front of him, and there is no gnome behind the tenth gnome. The ninth gnome has the tenth gnome behind him and the eighth gnome directly in front of him, and so on. Finally, the first gnome has the second gnome directly behind him, but there is no one in front of the first gnome.
The captor has a bag full of many black hats and many white hats. There is not necessarily the same number of black hats as white hats. (important) He randomly reaches into his bag and places a hat on each of the gnomes. This means that the tenth gnome can see everyone's hat except his own, the ninth gnome can see everyone's hat except his own and the tenth gnome's hat, and so on. The first gnome can see no one's hat.
The captor then takes out his gun and puts it to the temple of the tenth gnome. He asks the gnome, "What color is your hat?" If the gnome answers correctly, he lives and gets freed from the dungeon. If he does not, he dies. He continues up the line in this progression.
However, before placing the hats on the gnomes, he allows the gnomes to meet as a group and discuss a strategy to save as many of the gnomes as possible. How many gnomes can you guarantee to save, and with what strategy?
REMEMBER: When it is your turn to say the color of your hat you must ONLY say "white" or "black." If you say anything else, the king will shoot you and all of the remaining gnomes.
Re: Try this Puzzle
Re: Try this Puzzle - January 19th, 2016
Since each gnome can see all the hats in front of him and hear all the answers in back of him, here's what he does,
If the number of black hats in front of him plus the number of times a gnome in back of him said 'black' is even, then he says 'white'; otherwise he says 'black.'
Using this strategy, 9 gnomes can be saved.
Or we can say that using this strategy (N-1) gnomes can be saved.
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