Challenge of the Week: 2019 and 2020

By Department of Mathematics

Deadline: 11:59 PM on Sunday, Nov. 10

The Rules: 

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 bbajnok@gettysburg.edu or put it in Bela’s departmental mailbox by the above deadline. Consistently successful participants will receive the Paul Mugabi Mathematics Problem Solving Award.

The Problem: 

Is it possible to color each of the integers 1,2,3,…,2020 by orange or blue so that the sum of the orange numbers and the sum of the blue numbers differ by 2019? Is it possible to color each of the integers 1,2,3,…,2019 by orange or blue so that the sum of the orange numbers and the sum of the blue numbers differ by 2020?

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Author: Gettysburgian Staff

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