$N$ Hyenas are standing on a plane region in a forest. At $t=-1$, they see dead meat nearby. Being selfish, at $t=0$, each Hyena attacks the Hyena which is closest to it. All pairwise distances between them are distinct.
At most how many Hyenas can remain unattacked?
$N=1$, answer is $1$ since there is no other Hyena to attack the first Hyena
$N=2$, answer is $0$ (both attack each other)
$N=3$, answer is $1$
$N=7$, answer is $5$
$N=10$, answer is $7$
1) The closest pair is always under attack for $N>1$.
2) For odd $N$, it is easy to see that there exists at least $1$ Hyena which is not under attack.
Solve for $N=100$