There are 100 people on an island. Each person has an unlimited number of name-tags with his name on it. (Everyone has a different name)
When two people meet, each gives the other an unlimited number of all the name-tags that they currently have. (E.g. If person A meets person B they will both end up with having name-tags A and B with them. If person B then meets person C then persons B and C will both have all the name-tags A, B, and C while person A still only has name-tags A and B) [The name-tags never run out]
How many meetings between two people will it usually take until everyone has everyone's name-tag? Note: A person X has the name-tag of person Y if and only if there exist persons $A_1, A_2, ..., A_r$ such that $Y\rightarrow A_1\rightarrow A_2\rightarrow ... \rightarrow A_r \rightarrow X$ where $M\rightarrow N$ means M meets N and the meetings occured in exactly this order (from left to right).