by John Ehrke | Oct 4, 2019 | Problem of the Week
Will You Win? This problem was suggested by Brian Jacobs. Your friend has a game for you to try. He rolls two n-sided fair dice and you roll one n-sided fair die. You win if the number on your die is between the numbers on his dice, inclusively. For example, if he...
by Bethany Witemeyer | Oct 1, 2019 | Mu Sigma Events
This Wednesday (October 2) I am giving a talk over a card trick called Half and Half. Come to OSC 235 at 11:45 AM for a live demonstration of the trick as well as a discussion of some of the mathematics involved in making it work. I hope to see you there!
by John Ehrke | Sep 27, 2019 | Problem of the Week
Are There Infinitely Many? Are there infinitely many positive integers n such that n divides (that is, is a factor of) the number 2^(n)+1? Solutions are due by Thursday, Oct 3rd at 5:00 PM. Please submit all solutions to mathpotw@acu.edu. Solution to Are There...
by Wyatt Witemeyer | Sep 22, 2019 | Mu Sigma Events
The first meeting for Mu Sigma is coming up soon! (The Tuesday after Departmental chapel (10/8/19)) Here’s our planned agenda for the meeting. Show up so you’re informed all about Mu Sigma and future events! Introduce the officers (including me! :D) Look...
by John Ehrke | Sep 20, 2019 | Problem of the Week
Maximize the Area This problem is from the newsletter for users of the TI graphing calculators. Given a rectangular piece of paper, label the four corners of the paper A, B, C, and D (see figure below). Fold the vertex A so that it just touches the segment CD....
by John Ehrke | Sep 13, 2019 | Problem of the Week
Alexander’s Walk Home This problem is from Alexander Karabegov. Suppose that when Alexander walks home he always chooses one or the other of two routes. In one route he stays on a sidewalk that makes a right-angle turn and is tangent to a circular flower garden...
by John Ehrke | Sep 9, 2019 | Mu Sigma Events
Thank you to everyone who took the time to vote in the Mu Sigma nominations and elections this last week. The voting is now closed and we have new officers for the 2019-2020 school year. The list of officers is below. Congratulate them if you get a chance (or send...
by John Ehrke | Sep 6, 2019 | Problem of the Week
Find the Speed This problem is from Robert Stanfill by way of Tim Coburn. Outdoorsman Russ Rustic was rowing upstream on a river at a constant rate, thoroughly enjoying the scenic wonder of the area. In fact, he was so preoccupied with the beauty that he did not...
by John Ehrke | Mar 22, 2019 | Problem of the Week
Permutations Everywhere If A = {aij } is a symmetric (i.e., aij = aji) n by n matrix with n odd, and each row of the matrix is a permutation of the integers 1, 2, 3, … , n, prove that the main diagonal of A is also a permutation of 1, 2, 3, … ,...
by John Ehrke | Mar 1, 2019 | Problem of the Week
“Circular” Numbers? This problem is from Clayton Dodge. Prove that for any positive integer n, the number n2(n2-1)(n2-4) is divisible by 360. Submit your answers to mathpotw@acu.edu. Details for submissions can be found here. Solution Correct solutions...
