1. The problem statement, all variables and given/known data As a background to this...I have no experience with proofs at all. I did not take a formal geometry class in high school (took a shortened summer course that gave a VERY brief overview of proofs) and have not gotten to discrete math in university, so I really do not know how to approach/write proofs. At the top of my homework, it says: "For each problem solution, attempt to adhere to mathematical rigor. Proofs and arguments should be detailed and complete." I've never heard of mathematical rigor and after looking it up I still don't really know how to "conform" to it. Seems like it's some kind of standard for proofs. Here is one of the questions for my HW: "Six people enter a room. Either there are three people who know each other or there are three people who are strangers to each other. Prove the above statement. Where does a variant of the pigeonhole principle come in?" I don't quite know where to start - I looked up the pidgeonhole principle and didn't really understand how it applies to this problem. Maybe someone can point me in the right direction as to how to write a proof for this problem? This HW is due Thursday at 11:59 PM EST, help before then is very appreciated. 2. Relevant equations None that I know of. 3. The attempt at a solution ???