let's say we live in a "very strange" world of Facebook, in which everyone has $1000$ friends. In addition, every $n$ people will have exactly $\lceil{1000 * (\frac{1}{10})^{n-1}}\rceil$ friends in common if $n \leq 3$, not more than a friend if $n$ between (inclusive) $4$ and $1000$ and $0$ otherwise. How many people are there in this world? If there can be more than an answer, what is the lower and upper bound for this number?
PS: Friends and self are excluded from friends of friends.
PS2: I don't know the answer either :)
PS3: Assumed that there must be at least a person in this world
Edited:Just found a "bug" for this problem, say I'm A and my friends are A1, ..., A1000, friend in common of A, A1, A2, A3, A4 must be subset of friend in common of A1, A2, A3, A4, which is $A$.
I need to change the statement of the problem... :(