Every time you see a circle, inscribe a square inside it. Every time you see a square inscribe a circle inside it. Start with a unit square. What is the largest object (and its dimensions) whose area is less than 2^-99.5?

        The Problem Solving Competition uses problems submitted by professors and students from different campuses throughout the United States and abroad. Each month the competition sends out problems to participating institutions. 
         To submit your solutions to the current problems, give them to Cathie Trigueiro in 108 Deady. Your solutions should be clearly written and should show all of your work and contain some mathematics. A correct solution for each problem will qualify for a drawing. You don't have to solve all of the problems. Just submit the ones you can solve. The person with the winning draw will receive a ten dollar gift certificate to Pegasus Pizza. Of course, this competition is for undergrads only.

Without technology find all solutions to the following equation:

x⁷ sinx - 28x⁶ sinx - 5854x sinx + 4620sinx + 286x⁵ sinx - x⁷ + 28x⁶ -286x⁵ + 1302x⁴ -2351x³ - 406x² - 1302x⁴ sinx + 2351x³ sinx + 406x² sinx + 5854x - 4620 = 0

The only integer solutions are a set of 5 consecutive prime numbers.

       125 years of culture and conflict at the University of Oregon is an interesting topic. You can check it out at:


http://jcomm.uoregon.edu/~russial/cyberj/thenandnow/index.html