## Problem of the Fortnight

The problem of the week is back, but in a FORTNIGHT version! Similarly as in the previous semesters, a small prize will be awarded to the random correct solver, and a grand prize will be awarded at the end of the semester to the solver with the most correct submissions (or a random winner will be drawn in case of a tie).

Solutions (with explanations!) are to be submitted to Prof. Pavel Bělík, either electronically to belik@augsburg.edu, or to his mailbox or office in SCI 137A.

## Problem of the Fortnight #3:

A rectangle of unknown dimensions is cut into four pieces as shown in the figure below (not necessarily up to scale). Two of the four pieces have areas of *2* and *4* units as shown. Can the areas of the two other pieces be determined? If so, what are they?

They are due by Friday, October 25, 2013 (midterm break).

## Problem of the Fortnight #2:

Four cities, Angerville, Blabberville, Clutterville, and Deville, are located in the corners of a rectangle with sides 8 miles and 6 miles as shown in the left figure below. You are supposed to build a road (or roads) that allows you to travel from any one city to any other city. How long is the shortest road you can construct?

(An example might be a circle of radius 5 as shown in the second figure. The total length of this road is 2πr = 10π miles. Can you do better than that? Shortest solution wins!)

Submit your solution (with explanations!) by Friday, October 11, 2013.

## Problem of the Fortnight #1:

In a survey people are asked: “Do you think the new president will be better than the last one?”

Suppose *a* people say “better”, *b* say “the same” and *c *say “worse.” Sociologists calculate two measures of “social optimism”: SO_{1} = *a *+ *b*/2 and SO_{2} = *a *– *c*. If 100 people respond to the survey and SO_{1} = 40, find SO_{2}.

Submit your solution (with explanations!) by Friday, September 27, 2013.