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 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 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...
by John Ehrke | Feb 7, 2020 | Problem of the Week
Discover Something Let N be one more than the product of four consecutive positive integers. What can you say about N? Prove it. (Of course, what you say about N must have some substance. Trivial statements are unacceptable.) Please submit your work to...
