For about 11.5 years, I organized the Problem of the Month for the Hillsdale math department. My colleague Kevin Gerstle is the new puzzlemaster.
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.