A dwarf-killing giant lines up 10 dwarfs from shortest to tallest.
Each dwarf can see all the shortest dwarfs in front of him, but cannot see the dwarfs behind himself.
The giant randomly puts a white or black hat on each dwarf. No dwarf can see their own hat. The giant tells all the dwarfs that he will ask each dwarf, starting with the tallest, for the color of his hat.
If the dwarf answers incorrectly, the giant will kill the dwarf.
Each dwarf can hear the previous answers, but cannot hear when a dwarf is killed.
The dwarves are given an opportunity to collude before the hats are distributed.
What strategy should be used to kill the fewest dwarfs, and what is the minimum number of dwarfs that can be saved with this strategy?
My approach: 1st guy counts which color is max, says it, all others copy his ans. This way, we save at least 5, but I think we can optimize this, just can't figure out how....