There are two questions here: 1. What strategy guarantees the safety of the most dwarves? 2. What strategy is most likely to save the most dwarves?
For question #1, I can't guarantee the safety of more than five dwarves at this point.
Strategy A: Odd numbered dwarves call out the color of the dwarf ahead of them. Even numbered dwarves simply repeat what the last guy said. Guaranteed 5 dwarves saved, and 7.5 dwarves are saved on average.
Strategy B: Dwarf #1 calls out the majority color he sees in front of him. Everyone else simply repeats what #1 said. No matter the configuration, you are guaranteed to save at least 5 dwarves, and 6.23 dwarves are saved on average. Okay... that's inferior.
Strategy C: All dwarves, on their own turn, call out the majority color they see in front of them. If the number is tied, then instead call out the same color that was called last. I think this one still guarantees 5, but I haven't figured out an easy way to calculate the average number saved for all cases.Statistics: Posted by Mike — Fri Mar 24, 2017 1:38 pm
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