Department of Mathematics and Statistics
Problem of the Month
Problem 6, September 2014
The integers from 1 to 10 are randomly distributed around a circle. Prove that there must be three neighbors whose sum is at least 17. What about 18? What about 19?
Please submit your solution for this month problem no later than 15 of the next month. Try to keep
your solution to less than two pages. My office is in MSC 426 and my email address is
firstname.lastname@example.org You may also put your solution in my mailbox (Mihai Staic).
If you want to propose a problem please contact me by email or in person.
Problem 5, September 2013
a) Place a knight on each square of a 4x4 chessboard. Is it possible for each knight to simultaneously make a legal move so that each knight ends up in its own square?
b) Place a knight on each square of a 7x7 chessboard. Is it possible for each knight to simultaneously make a legal move so that each knight ends up in its own square?
Problem 4, April 2013
Determine all the differentiable real functions f from R to R whose composition with themselves, fof, is the original function f.
Problem suggested by Professor Sam Nadler from The University of Toledo. Correct solutions were submitted by: Nate Day and Rob Kelvey.
Problem 1, August 2012
A page (two sides) is torn from a paperback novel. The sum of the remaining page numbers
is 15000. Which page was torn out? (Rasor-Bareis Exam 1996) Solution
Correct solutions were submitted by: Mike Hughes, Devin Bender, Suzanne Hirsel. There were
other students that submitted partially correct solution.
Problem 2, September 2012
Consider a bounded solid S that has the following property: Whenever we intersect S with a
plane the intersection is either the empty set or a point or a disk. Show that S must be a
sphere (a ball).
Problem 3, October 2012
Find all functions f from R to R such that f(x+y)=f(x)+f(y) and f(xy)=f(x)f(y) for all x and
y in R.