I am not sure I can strictly define recreational mathematics. But we all feel what it is about: puzzles, problems you can ask your mathematical friends, problems that will bother them for a couple of hours, and then they will get them (or not?). Problems to distract yourself from research. Sometimes, however, these problems lead to some ideas and concepts connected to "serious mathematics". I adore this kind of problems and, with holidays approaching, I let myself surf on Internet for some new problems to distract myself a little near the Christmas tree. I usually look at some blogs but my search is very chaotic. I'll try to formulate more precisely what kind of problems I'm searching for: there are two kinds of them.

First, good mathematical problems. So good that you can talk about the solution for an hour although the formulation could be really easy.

*Example: the old Arnold's question about the perimeter of a banknote. By folding up a banknote, we decrease the area of the polytope obtained. But can we increase the perimeter? The answer is yes, and we can increase it as much as we want. The proof is beautiful and doesn't need any knowledge of higher mathematics although it is not at all trivial.*

Second, problems giving some publicity for higher mathematics. I will give an example - hat puzzle.

*A sultan decides to give a test to his sages (a countable number of sages actually!). He has the sages stand in a line, one behind the other, so that the person in a line sees everybody before himself. Yes, the sages are clever but also they have a very good vision. He puts the hats on them: white or black. Then, the sages cry (all at one time) the color that they think they are wearing. Everybody who is wrong will be killed. The question is, can the sages achieve the result that only the finite number of them will be killed?*
I won't spoil you the pleasure giving the answer but this puzzle in some sort opens a path to some serious mathematics and can be a good pretext to explain it on the seminar for high-school student (or even to undergraduate).

I search for problems that are easy to formulate and not trivial to solve, and that could give a nice pretext to talk about them for a couple of hours for undegraduates. In other words, I search for problems that could make a good advertisement of "serious" mathematics for high-school students that love puzzles.

My question is -- are there any journals (I think, Mathematical Intelligencer can be one of the possible answers..) that publish some kind of research articles on the subject? Maybe some blogs I do not know?

Any links or suggestions will be welcomed.

Scientific Americanwill contain good recreational problems at various levels. $\endgroup$ – Noam D. Elkies Dec 22 '13 at 1:27