Evil wizard...

GameMaster · Site Regular Joined: 20 Apr 2006 Posts: 55

There is a village of wizards and a village of dwarves. Once a year, the wizards go over to the village of dwarves and line all the dwarves up in increasing height order, such that each dwarf can only see the dwarves smaller than himself. The wizards have an infinite supply of white and black hats. They place either a white or black hat on the head of each dwarf. Then, starting with the tallest dwarf (in the back of the line), they ask each what color hat he is wearing. If the dwarf answers incorrectly, the wizards kill him (the other dwarves can hear his answer, but can't tell if he was killed or not). What strategy can the dwarves use to minimize the number of dwarves that are killed? What is the most number of dwarves that will be killed using this optimal strategy?

some-g · Site Admin Joined: 14 Mar 2005 Posts: 190

Well, the best strategy would be to take off the hat and look at it.

Next best would be for the dwarves to call out two colors, first their "guess" as to what color the hat is, followed immediately by the color of the dwarf's hat in front of him/her. That way the tallest dwarf would have 50/50 chance of living and everyone else would live. Max deaths 1

GameMaster · Site Regular Joined: 20 Apr 2006 Posts: 55

Neither are allowed. I suppose, I need to make that change the next time I tell the riddle.

GameMaster · Site Regular Joined: 20 Apr 2006 Posts: 55

Hint 1: The darves have a system. But, this should obvious to anyone.
Hint 2: The first ideal solution has 50/50 chance of getting the first dwarf killed, but will save all the others.

GameMaster · Site Regular Joined: 20 Apr 2006 Posts: 55

No one?

Alright.... Here's the solution:
http://www.game-master.us/phpx-3.4.0/126.php?riddle_id=42

outsider · New Member Joined: 21 May 2006 Posts: 10

Very very nice.

Unfortunately I didn't read the conditions thoroughly and lost the opportunity to enjoy thinking of it.

GameMaster · Site Regular Joined: 20 Apr 2006 Posts: 55

Yeah, when I first found it my gut reation was to kill half of them... Then I started to think about it somemore. I was very close when I finally gave in and asked what the answer was.