by John Ehrke | Nov 13, 2020 | Problem of the Week
A Fractional Sum Given a positive integer n, which integers can arise as the sum where xi is a strictly increasing sequence of positive integers? Please submit all solutions to mathpotw@acu.edu by 5:00 PM on Thursday, Dec 2nd. This will be our final problem of the...
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 | 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...
