Troll captures some dwarves (riddle)

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From Corey Fisher, a deadly Tolkienesque problem:

A giant troll captures 10 dwarves and locks them up in his cave. That night, he tells them that in the morning he will decide their fate according to the following rules:

The 10 dwarves will be lined up from shortest to tallest so each dwarf can see all the shorter dwarves in front of him, but cannot see the taller dwarves behind him.
A white or black dot will be randomly put on top of each dwarf’s head so that no dwarf can see his own dot but they can all see the tops of the heads of all the shorter dwarves.
Starting with the tallest, each dwarf will be asked the color of his dot.
If the dwarf answers incorrectly, the troll will kill the dwarf.
If the dwarf answers correctly, he will be magically, instantly transported to his home far away.
Each dwarf present can hear the previous answers, but cannot hear whether a dwarf is killed or magically freed.
The dwarves have the night to plan how best to answer. What strategy should be used so the fewest dwarves die, and what is the maximum number of dwarves that can be saved with this strategy?

Extra credit: What if there are only five dwarves?

 

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townie is a genius so I expect him to nail this one

 

[TownieDeac]

have the tallest, first dwarf indicate via some sort of code like black is odd, white is even and more or less sacrifice himself with the communication of that information to the rest of the dwarves

so if the first dwarf says white, then the next dwarf also sees an even number of white dots, he knows he's got a black dot

set up a similar scheme for 5 dwarfs

 

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Answer at bottom of this link

https://fivethirtyeight.com/features/what-are-the-chances-well-meet-for-lunch/