By Department of Mathematics
Deadline: 11:59 p.m. on Sunday, Nov. 3, 2019
The contest is open to everyone. Individuals or teams of at most three members may submit solutions. Do not discuss the problem with anyone other than members of your team. You may use any source, written or electronic, but all sources must be properly cited. You may use any computational tools. Your solution will be graded on a 0–4 point scale. All your assertions must be completely and fully justiﬁed. At the same time, you should aim to be as concise as possible; avoid overly lengthy arguments and unnecessary components. Your grade will be based on both mathematical accuracy and clarity of presentation. Either send your solution to firstname.lastname@example.org or put it in Bela’s departmental mailbox by the above deadline. Consistently successful participants will receive the Paul Mugabi Mathematics Problem Solving Award.
At a certain mixer at the College Ballroom, attended by quite a lot of students, it turns out that there are no four students, A, B, C, and D, so that A knows B, B knows C, and C knows D (we assume that acquaintances are mutual). As host, your goal is to send some students to the Orange Room and some others to the Blue Room in such a way that no two students know each other in any of the three rooms (the Orange Room, the Blue Room, and the rest of the students in the Ballroom). Is this always possible?