On the planet of liars and truth-tellers, the government hired \(100\) truth-tellers and \(100\) liars. Everyone has at least one
friend, and if one alien is friends with another, then the feeling is
mutual.
Exactly \(100\) of them said, “All my
friends are honest,” and the other \(100\) said, “All my friends are
liars.”
What is the smallest possible number of friendships between an honest
alien and a liar?