Coffee Hour Problems

(How many mathematicians does it take to solve interesting math problems when they are being fueled by coffee?)

Since November 2017, I regularly leave a math problem on the table where the departmental coffee hour is held. I usually do it on days when I'm in charge of coffee and cookies, and I think this should become a departmental tradition!

Here you can find a list of these problems and their solutions. They come from various sources, such as math olympiads, book problems, communication with others, and sometimes my own head. The difficulty and prerequisites are also varied. The only constants are that the problem and solution should always fit a single page and should be related to coffee and cookies, preferably using food emoji instead of letter variables because that makes it look really annoying.