I organize the Problem of the Month for the Hillsdale math department. To submit a solution, come to my office (DSC 106) and tell me all about it! At the end of the year, the student with the most correct solutions will receive a prize.
As of April 2017, Problem of the Month has expanded to a "Puzzles and Fun" newsletter, which now includes a chess puzzle and a joke. Thanks to Sam Cassels, Thomas Reusser, and Dietrich Balsbaugh for contributing!
Current P&F (May-August 2025) here.
Past problems and solutions:
May 2023: problems and solutions. Here is a paper proving that the strategy given in the solution is optimal.
November 2018: problems (solutions missing)
October 2018: problems (solutions missing)
September 2018: problems (solutions missing)
December 2014: problem and solution. See also the classic paper on which the problem is based.