By Department of Mathematics
Deadline: 11:59 PM on Sunday, Oct. 20
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.
For positive integers n and m, the squares of an n-by-m grid are each painted orange, with the exception of one corner square that is painted blue. Your goal is to paint the entire grid blue, but you must do this one square at a time, and a square can only be painted blue if it has exactly one or three blue neighbors. (Two squares are neighbors when they share a side.) Determine all values of n and m for which you can achieve your goal.