# Examples of Good Mathematical Games for a Mathematical Olympic

As a crazy idea in a coffee break after a boring lecture I suggested my students and colleges that we can have some fun in our department by participating in a "Mathematical Olympic Games". They supported the idea extensively and now we are in choosing/designing games phase. Beside usual games with mathematical aspects like Sudoku, Rubik Cube, Origami, etc. I suggested that it could be very useful if we invent some games inspired by usual material of undergraduate courses like Algebra, Analysis, Number Theory, Graph Theory, etc. because participating in such games helps students to become more familiar with actual applications of what their teachers are trying to teach them. Also if teachers are amongst participants/referees they can help students by their advisement too.

Question. What are good examples of mathematical games inspired by the usual subjects of undergraduate courses? Please specify that for improving abilities in which undergraduate courses your suggested game is good.

Remark. All other suggestions for interesting games are welcome.

• So this is a local event? Not like IMO or something like that? Then you might consider NIM-games for the pure joy of recursive thinking. Actually that would be accessible to high schoolers, so may not be your cup of coffee. Mar 25, 2014 at 8:10
• @JyrkiLahtonen It is a local event in our university. We have a plan to spread the domain of participants to other universities in the short time. NIM is an interesting game but unfortunately there is an easy winning strategy for it. We are thinking on more complicated games in order to have an exciting competition.
– user230
Mar 25, 2014 at 10:20
• Nim can also be played using infinite ordinals; while there is a winning strategy it takes quite a bit more sophistication to implement it. Mar 25, 2014 at 13:40
• @KevinO'Bryant (+1) It is a really interesting example of a set theoretic game simple enough for undergraduate students to understand and complicated enough for having an exciting competition on it. Existence of a winning strategy or a solution algorithm is not a problem if it is somehow non-trivial/strange.(e.g. There is an algorithm for solving Rubik cubes but it is still an exciting game) Would you please add some link/reference for the exact explanation of the ordinal-valued NIM and its winning strategy?
– user230
Mar 25, 2014 at 13:52
• What do you want? Games with interesting mathemathical analysis, to be done/checked by the participants? Something else? Mar 26, 2014 at 1:25

Some possibilities coming from algebra are
https://mathoverflow.net/questions/93276/a-game-on-noetherian-rings
and
http://arxiv.org/abs/1205.2884
though it depends on how much algebra the students will have been introduced to at that point.

Another possibility is the game Hex (http://en.wikipedia.org/wiki/Hex_(board_game)) since here the impossibility of a draw is related to the Brouwer fixed point theorem.

• Welcome to MESE Tobias. Your suggestions are very nice. In order to be fair we will distribute participants in different groups including 1st year undergraduate students, 2nd year and so on. For which group do you suggest your algebra games normally?
– user230
Mar 25, 2014 at 10:15
• @SaintGeorg It depends on how much algebra has been covered at those points (this varies a lot from place to place). Probably most places nobody will have heard about noetherian rings at this point, but the game can be played without mentioning this (just choosing polynomial rings which at least many places will have been introduced by the third year). Mar 25, 2014 at 10:21
• Useful guidance. Thanks.
– user230
Mar 25, 2014 at 10:24

There are very simple graph theoretic games like Criss-Cross, invented by Sam Vandervelde as far as I know, and harder slightly related games like Sprouts.

Well-known games like SET are actually games on 4-dimensional geometry; defining lines and planes and so on can be a lot of fun. You can emphasize the geometry a bit with some of the games like Planet in Brian Conrey et al. There's also some great geometry in the game of Spot It! and you can easily ask questions about projective planes.

The Tower of Hanoi is a classic puzzle which has a lot of mathematical aspects: recurrence relations, combinatorics, binary number system... It can be analyzed using Graph Theory... Also the classical Peg Solitaire can be analyzed using Group Theory.

How about a game based on the Traveling Salesperson Problem from graph theory? Put pedometers on each of your participants. Pick several local landmarks, provide those locations to your competitors, and see who can visit -- by walking -- all the landmarks in the least amount of distance, as measured by the pedometers.