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 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...
by John Ehrke | Feb 22, 2019 | Problem of the Week
Problem 13 – February 22, 2019 Some Are Not That Far Away Consider any five points P1, P2, P3, P4, and P5 in the interior of a square of side length 1. Denote by dij the distance between points Pi and Pj when i is not equal to j. Prove that at least one of the...
by John Ehrke | Feb 8, 2019 | Problem of the Week
Problem 12 – February 8th, 2019 Is It Really One-seventh? I learned of this problem in a session on mathematics and art at the 2003 joint AMS/MAA meeting. Given any triangle ABC, construct a line from each vertex to the opposite side as indicated in the figure below....
