by John Ehrke | Oct 30, 2020 | Problem of the Week
Probability of Losing This problem is from Grant Fikes. In a certain game played with four dice, a player wins points if the player rolls the four dice and gets at least two of the same number ( for example, {1,2,2,5}, {2,2,3,3}, {1,3,3,3}, etc.) or has at least three...
by John Ehrke | Oct 16, 2020 | Problem of the Week
Give and Take On the first hole of a golf match, Jason lost to Mark as many dollars as Mark had with him at the golf course after paying his green fee. On the second hole, Mark lost to Jason the amount of money that Jason still had after paying his loss on the first...
by Myriam Gutierrez | Oct 15, 2020 | Mu Sigma Meetings
Hello everyone! Today we had our first Mu Sigma meeting of the semester! Thank you to those who showed up and shared some awesome ideas for possible events for the year. If you missed the meeting today, below is a report of the minutes and some discussion highlights:...
by Myriam Gutierrez | Oct 13, 2020 | Mu Sigma Meetings
Hey all! We will be having our first Mu Sigma meeting of the semester this week! Here are some details for the upcoming event: Oct. 15, 2020, 11:20am – 11:50, OSC 365 Agenda: Officer Introductions Major and Track Fun comment! Let’s get to know each other!...
by John Ehrke | Oct 2, 2020 | Mu Sigma Events
Divisible by 9 This problem is from Alexander Karabegov. Given an integer m, suppose that the integer n is obtained from m by permuting its digits. For example, if m = 171243, then n could be 711234, or n could be 432117, and so on. Show that the difference m –...
by John Ehrke | Sep 26, 2020 | Mu Sigma Events
Symmetric Functions II This problem is from Alexander Karabegov. Solve the following system of equations (you may want to look back at the previous Problem of the Week): x3 + y3 = 9 5xy = 2×2 + 2y2. Please submit all solutions to mathpotw@acu.edu by 5:00 PM on...
by John Ehrke | Sep 17, 2020 | Problem of the Week
Symmetric Functions I This problem is from Alexander Karabegov. Given a quadratic polynomial x2 + p x + q with two real roots s and t, express the following functions of s and t as polynomials in p and q. s + t st s2 + t2 s3 + t3 Please submit all problem solutions to...
by John Ehrke | Feb 28, 2020 | Problem of the Week
An Easy Fermat Case Find all solutions in integers of x2 + y2 = z2, with x, y, and z in arithmetic progression. Please submit all problem solutions to mathpotw@acu.edu before 5:00 PM on March 5th.
by Jackson Shoultz | Feb 23, 2020 | Mu Sigma Events
Hello everyone! Thanks to those of you who were able to make it to our meeting on the 11th! Below is a report of the minutes of that meeting and some discussion highlights: 11 February 2020: 11:41am-11:56am From Dr. Ehrke: MAA signups need to be done by the end of...
by John Ehrke | Feb 21, 2020 | Problem of the Week
Where Does It Happen? This problem is from Jason Holland. Let x1, x2, x3, x4 be real numbers such that x2 – x1 = x3 – x2 = x4 – x3 = 1. Prove that the product x1x2x3x4 is never less than -1, but can equal -1. Find all lists (x1, x2, x3, x4) for which...
