Math Problem of the Week
The Mathematics Problem of the Week is intended to give students an opportunity to use the knowledge they gain from their classes to solve interesting mathematical problems from various areas of mathematics. Submissions are scored, and the student with the highest cumulative score each semester will be award a $100 gift certificate to the Spirit & Supplies Shoppe!
The problems for the Fall 2014 semester are posted below.
For more information about the Problem on the Week, please contact Dr. Nick Wintz.
Problem 1: Let b and c be real numbers, and d fine the polynomial P(x) = x2 + bx + c. Suppose that P(P(1)) = P(P(2)) where P(1) ≠ P(2). Find P(4).
Problem 2: Find the value(s) of a such that 1/log2a + 1/log3a + 1/log4a = 1.
Problem 3: Evaluate .
Problem 4: A six-sided die has one of the letters A, B, or C written on each of its sides. The letter A is written on 3 sides, B is written on 2 sides, and C is written on 1 side. The die is rolled until a C comes up as the result of a roll. What is the probability that A appeared as the result of at least one prior roll?
Problem 5: Evaluate .
Problem 6: Find all right triangles whose sides are positive integers and whose perimeter is numerically equal to their area.
Problem 7: Evaluate .