Math problem of the day

Since I’m taking my last semester of classes I realized that I might never take a math class again :(.  So, I was thinking to keep my math skills sharp I might start a problem of the day (or in some other increment).  I really don’t want to loose my mathematics skills.  Also, I can’t find anything like this for more of the advanced math like DE and probability theory stuff.  I’ll post the question along with my solution.  This might remind you of Project Euler, but I’m thinking that I’d like to keep the problems (at least for me) to those that require less computers and more mathematical tools.  So, basically they can be solved entirely with a pen and paper without a computer in less than a half hour.  Also, I’d like to then expand my own math skills so I might have a day where I find a problem from some graduate level math.  If I actually find I do this I might start its own page.