By Department of Mathematics
Deadline: 11:59 PM on Sunday, Oct. 6
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 email@example.com or put it in Bela’s departmental mailbox by the above deadline. Consistently successful participants will receive the Paul Mugabi Mathematics Problem Solving Award.
Find all positive integers n for which it is possible to color each of the integers n, n + 1, n + 2, n + 3, n + 4, and n + 5 by either orange or blue so that the product of the orange integers equals the product of the blue integers.