In a group of $k$ people, some are acquainted with each other and some are not. Every evening, one person invites all his acquaintances to a party and introduces them to each other (if they are not acquainted). Suppose that after each person has arranged at least one party, some $2$ people don’t know each other. Prove that they don’t meet each other in the next meeting.
Can this be solved using PHP?
I began by assuming that some arbitrary person out of the $k$ available has thrown a party, then everybody who comes there will know everybody else, so if they are not acquainted after this party, it means they won't meet at the next party.
Is my working right?