# Recreational mathematics: where to search?

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.

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This looks like a community-wiki problem of the "potentially-big list" type. To add to the list, any of Martin Gardner's books based on his "Mathematical Games" columns in Scientific American will contain good recreational problems at various levels. – Noam D. Elkies Dec 22 '13 at 1:27
@Noam D. Elkies Thank you for your comment, I will certainly look it up! – Olga Dec 22 '13 at 10:44
Tanya Khovanova's blog blog.tanyakhovanova.com has a lot of nice recreational math. – Richard Stanley Dec 23 '13 at 18:22
@ Richard Stanley Yes it has, I love this blog!!! This post was inspired by it. – Olga Dec 25 '13 at 12:21

## 9 Answers

There is a journal called Journal of Recreational Mathematics, but I do not like some of the articles it contains. You might do better with The American Mathematical Monthly, which often publishes papers on what can be considered recreational mathematics. (Here I define recreational mathematics as those that can be done by amateurs. As was mentioned in the commnents above, the mathematics popularized by people such as Martin Gardner can be considered recreational mathematics.)

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Thank you for the link to the Journal of Recreational Mathematics, I will look it up. AMM is a great journal but it usually reexplains the classical theorems. They are proven in a nicer and simpler way. For example, the irrationality of $e$ or something in the genre... Although I would prefer problems which take inspiration in games, puzzles etc. But I'm pretty sure one can find something like this in AMM too! – Olga Dec 22 '13 at 10:51
I believe JORM has ceased publication. – Gerald Edgar Dec 13 '15 at 14:49

Books on recreational mathematics can be found at QA95 (Library of Congress) and 793.73/4 (Dewey Decimal System).

Martin Gardner has been mentioned; terrific as his books are, I think those of Ian Stewart are even better. Peter Winkler also has a couple of excellent books.

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Dear Gerry. I've just hyperlink the name of Ian. I hope you don't mind. – Amir Asghari Dec 22 '13 at 18:26
In fact, "Mathematical Puzzles" by Peter Winkler is a perfect match for this question. Of course, it only contains a finite number of problems... – Victor Protsak Dec 22 '13 at 18:56

This is somehow a copy of my answer to a closely related question:

G4G (Gathering for Gardner) is a Foundation that is worth to connect with. From 2010, people around the world celebrate the birthday of Gardner and G4G somehow links all of them together. Just visit G4G and you get many useful ideas, books, journals, venues and you may share your own ideas.

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As you speak russian, take a look at the problems of Турниры Городов (Tournaments of cities.). I do believe that you can find the most interesting collection of such problems. There is a real tradition for such kind of problems and puzzles in Russia.

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Yeah, thank you, of course I've heard of Tournaments of cities, even participated in my youth. There are although some inconveniencies: as you said, it's in Russian (for me it's not a problem but for the community it is -- aren't the problems of Tournaments of cities translated to English?... it will be of a big help to community!), and also there are no solutions, no explanations. I would prefer the papers where everything is explained, Tanya Khovanova's article called "A line of Sages" published in The Mathematical Intelligencer, November 2013 will be a great example. – Olga Dec 22 '13 at 10:48
Some of them, the most recent ones, are translated in English: math.toronto.edu/oz/turgor/archives.php – smyrlis Dec 22 '13 at 11:02
this is great news, thank you! – Olga Dec 22 '13 at 11:03
Interestingly, They are also translated in Persian. But, I assume you cannot read Persian :-) – Amir Asghari Dec 22 '13 at 18:42
@AmirAsghari: Iran has also a notable tradition in mathematical olympiads. – smyrlis Dec 22 '13 at 18:44

"Tournaments of cities" mentioned in one of the answers just reminded me of a very lively magazine, again with Russian origin, that is unfortunately not published anymore: Kvant (Quantum). It is not a journal of recreational math as such. But it indeed helps your high-school students re-create math. It also has (had) a problem section that I believe would be a good match for what you are looking for.

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There are three books publishing selections from Kvant in English translation in the AMS's 'Mathematical World' series. – Marius Kempe Dec 22 '13 at 23:01

Also try math.SE: http://math.stackexchange.com/search?q=recreational (Perhaps more recreational material appears there than here.)

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See:

1) Proceedings of the recreational mathematics colloquium I, University of Évora, Portugal, April 29-May 2, 2009.

2) Proceedings of the recreational mathematics colloquium II, University of Évora, Portugal, April 27-30, 2011.

[Items 1 and 2 are not currently available online but are obtainable from the editors at http://rmm.ludus-opuscula.org/Home/Index ].

3) Recreational mathematics colloquium III (2014) is available online in PDF format (4 issues) at the above website.

4) Recreational mathematics IV (2015) is also available online in PDF format (4 issues) at the above website.

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I don't know if this answers your question, but the first place that I would look would be Wikipedia. There is a page of recreational mathematics. I would focus on the authors on that page, but there is also a page underneath that one, "Category: recreational mathematicians," which may be an even better place to start from scratch.

In fact, the Wikipedia article does mention three journals that give recreational mathematics problems: Eureka, The Journal of Recreational Mathematics (which stopped publishing in 2014), and Recreational Mathematics Magazine.

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Miklós Schweitzer is a contest about research level problems, look some problems. Actually there a book about it: Contests in Higher Mathematics.

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