Suppose we are considering a party that has p people at it. A person at the party is dened to be a rock star if E individual at the party knows the rock star, but the rock star knows m of them. There are certainly people at the party who may not know one other, so, for example, if Bob knows Sally but Sally does not know Bob at a party with 30 people, this alone does not make Sally a rock star; she would have to know nobody at the party, and everybody at the party would have to know her. Only then would she be considered a rock star. There is, at most, one rock star at the party (there may not be a rock star at all!). After all, if there was more than one rock star, then they would know each other! Your task is to locate the rock star, if one exists, at a party, by asking only one type of question asking a party-goer whether they know some guest. Each person must tell the truth. For example, if Dave and Sally are two people at the party, you can ask Dave whether he knows Sally, and he must tell the truth. Using mathematical induction, prove that if there are p Z 2 people at the party, then you can nd the rock star (if one is present), with no more than 3 (p 1) questions. So, for instance, if there are 2 people at a party, then we should be able to identify whether or not a rock star is present by asking 3 or fewer questions