Ten gangsters are standing on a flat surface, and the distances between them are all distinct. Suddenly, each of them fatally shoots the one among the other nine gangsters that is the nearest. What is the maximum possible number of surviving gangsters?
(In reply to
A guess (spoiler?) by Steve Herman)
I agree with everything you say except 7 survivors is not difficult.
Place 7 gangsters at the vertices of a regular heptagon. Draw a circle from each to his neighbors. This gives 7 regions (skinny footballs) that the remaining gangsters go. They do need to be placed close to the center.
Then move the outer gangsters by epsilons so the distances are unique.
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Posted by Jer
on 2019-05-06 12:25:03 |
re: A guess (spoiler?)
