ACU Mathematics Problem of the Week
Problem 5 – February 20th, 2018
The Problem of the Week competition, sponsored by Mu Sigma, is now live. This week’s problem can be found below or slips of paper with the problem description can be found on the main bulletin board in the math department. Students have two weeks from issuance of the problem to construct a solution. Simple answers will not suffice for most problems. Your solution must demonstrate a solution method and communicate some understanding of that method to qualify. Students with correct responses will be identified on this blog and the math bulletin board, and the student or students with the most correct responses during the year will be recognized at the departmental dinner each spring. This competition is open to all students regardless of major or affiliation with the department. You may return your solutions to Gaye in the math office any time before noon on the final day.
Issued: Tuesday, February 20th
Return Solutions By: Monday, March 5th
The Average Birthdate of the President
Thanks to Dr. John Ehrke for suggesting this problem.
An online article recently proclaimed that the average birthdate of the American presidents from Washington to Trump considering only the month and date of birth (not the year) was July 4th. How patriotic! The article described their method for calculating the birthdate as to create a list of days numbered 1-366 with January 1st listed first and December, 31st listed last. The leap year date was included in the listing. The author then averaged all those dates and arrived at approximately 185, which falls on July 4th.
Questions:
- Is the article’s conclusion correct? If so, defend their conclusion with a mathematical justification and a more rigorous analysis.
- If you think the article’s conclusion is incorrect, explain why you think so. Carefully detail your own procedure for arriving at your answer.
The winner of this contest will not be the first one to respond, but the one whose work most thoroughly convinces the judges of their answer.
A table of birthdates for all the presidents is included below.
http://blogs.acu.edu/mu_sigma/files/2018/02/presidentbirthdays.png
