Given a set of events that do not necessarily occur with the same probability, calculate the probability that at least a given number of those events will occur.
You are developing a matchmaking system for your online game and you prioritize that strangers play against each other. This means that if two players $a$ and $b$ are not friends, then they should be in opposite teams. Since you want some diversity you'll allow that friends are grouped in different teams (So two strangers are always in different teams while two friends might be). Develop an algorithm that determines wheter such a grouping is possible given the needed friendship informations.
You are dealing with a domino set, in which the tiles are of different height. Given an arrangement of tiles, determine how many dominoes will fall after toppling the first (left-most) domino.