by John Ehrke | Jan 27, 2020 | Problem of the Week
Win the Contest This problem is from Grant Fikes. Every year at the annual Winter Wizard World conference, there is a contest for student teams from each of the wizard training schools. This year each team has five student members, and each member of each team has...
by John Ehrke | Nov 1, 2019 | Problem of the Week
What Does This Thing Do? Determine what the following algorithm does, and then prove that it does what you think it does. {Input: a real number a and a positive integer n.} begin p := 1 q := a i := n while i > 0 do if i is odd then p := p*q {Do the next two steps...
by John Ehrke | Oct 11, 2019 | Problem of the Week
Two Handy Inequalities This problem was suggested by Alexander Karabegov. Prove the following inequalities are true for all positive real numbers x and y, with equality holding if and only if x = y. Hint: (x-y)2 is greater than or equal to 0. Please submit all work to...
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 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 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....
