10 dwarves where hanging around and a big giant came, he said that tomorrow he will put them on a column, each of them facing forward. He will put them white and black hats, and ask from the last to the first which color is his hat, if one told it right, he live, if not he die. The dwarves had a night to make a plan, and they made a plan that 9 of the dwarves would 100% live, and the last one had 50-50.
What was this plan?
Some stuff to know:
They can only say White or Black.
They're all facing forward, so the last one can see all the 9 hats of his friends, and the 9th could see all the 8 hats, and so on.
Gear300
Aug18-08, 07:42 PM
Is the giant a black hole?
rootX
Aug18-08, 07:56 PM
They can decide to pronounce white/black differently depending upon what's the color of next dwarf hat.
If the next dwarf has white then take longer time to say your hat color and if it is black say it faster.
jimmysnyder
Aug18-08, 07:58 PM
Each of the 10 told the color of the hat on the one directly in front.
humanino
Aug18-08, 09:01 PM
Assign 0 to white and 1 to black (for instance). The first one (last in the row) sees all other hats, adds all the numbers, and says b or w according to the parity of the sum of other hats. 50/50% will it match his own hat. Later on, the next in the line can deduce the color of his own hat, by the knowledge of all hats in front of him.
Sakha
Aug19-08, 01:18 AM
They can decide to pronounce white/black differently depending upon what's the color of next dwarf hat.
If the next dwarf has white then take longer time to say your hat color and if it is black say it faster.
Thats a way, but what we want is a real logical answer. Thats why its with giant and dwarves, to state the control the giant has over the dwarves.
Each of the 10 told the color of the hat on the one directly in front.
What if the one on your back tells you're black, and the guy in front of you is white, will you save yourself or the one in front of you.
Assign 0 to white and 1 to black (for instance). The first one (last in the row) sees all other hats, adds all the numbers, and says b or w according to the parity of the sum of other hats. 50/50% will it match his own hat. Later on, the next in the line can deduce the color of his own hat, by the knowledge of all hats in front of him.
Yep you got it.
The exact answer:
The last one says white if he looks a even number of blacks, and the others deduce from it and keep it going.