A friend of mine recently asked me for some suggestions for games or other activities for children that would help promote quantitative reasoning or mathematical skills, while remaining fun to play (i.e. more than just homework-type questions poorly disguised in game form). The initial question was focused on computer games (and specifically, on iPhone apps), but I think the broader question would also be of interest.

I myself have not seriously played these sorts of games for years, so I could only come up with a few examples immediately: the game “Planarity“, and the game “Factory Balls” (and two sequels). (Edit: Rubik’s cube and its countless cousins presumably qualify also, due to their implicit use of group theory.) I am hopeful though that readers may be able to come up with more suggestions.

There is of course no shortage of “educational” games, computer-based or otherwise, available, but I think what I (and my friend) would be looking for here are games with production values comparable to other, less educational games, and for which the need for mathematical thinking arises naturally in the gameplay rather than being artificially inserted by fiat (e.g. “solve this equation to proceed”). (Here I interpret “mathematical thinking” loosely, to include not just numerical or algebraic thinking, but also geometric, abstract, logical, probabilistic, etc.)

[Question for MathOverflow experts: would this type of question be suitable for crossposting there? The requirement that such questions be “research-level” seems to suggest not.]

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5 May, 2010 at 4:57 am

Tim van BeekI’d add to chess that the demonstration of a tactical strike, namly that a certain move will win whatever the reaction of the opposing player is, is close to the encounter of your first mathematical proof.

And the mastery of the game requires hard work, concentration etc. which is close to what learning mathematics is like. The game itself however is more about intuition that about logic (does it sound familiar?).

The advanced dungeons and dragons games have a complex rule system that require basic probability reasoning and game theory (and the pen-and-paper versions use dodecahedron and icosahedron as dice :-)

5 May, 2010 at 6:21 am

MiguelWhat about Chess?

5 May, 2010 at 10:34 am

MiguelConsider the following modification of standard chess. The rules are the same except that each player makes two moves every turn. Show that there is no wining strategy for black.

5 May, 2010 at 11:03 am

JairHere’s a very simple game I invented that can be played with only a pad of paper and two differently colored pencils. It’s essentially a two-dimensional version of that old game of picking a number from one to a hundred and trying to get closest to some unknown number. Two players alternate putting dots of their color inside a square (or circle, or other shape) until they each have a certain number (say three) of dots. Then some kind of random mechanism is used to mark a random point in the shape (for example, closing your eyes and dropping a pencil onto it). Then the players find the point that is the closest to the random pencil mark; the owner of that color wins a point. Thus the strategy is to cover the largest area on the shape in the sense of having a point of your color closest to every point in that region. This can be modified to be played with any number of players.

7 May, 2010 at 4:33 am

RonAn alternative angle of attack is to start with the games the kids play and point out how math can inform their choice of strategy in the game.

In simple facebook-games such as farmville and social city, avid players publish spreadsheets that work out what goods in the game maximize their profits, given its value, production cost and production time. (In social city for instance, it reveals that gamers are rewarded for taking many production jobs with a short timescale, keeping them online for as long as possible. An important part of the game’s business model no doubt)

In other games, it’s useful for the gamer to consider how many tries are needed to find the right combination of two items, given a choice of n items. The same goes for probability of success in attacking an opponent in certain games.

7 May, 2010 at 9:40 am

Carnival of Mathematics #65 « Maxwell’s Demon[…] who can understand and apply the mathematical ideas. The great Terrance Tao gives some ideas on games that help you develop this mathematical thinking. From Let’s Play Math, you can even have a bit of fun with […]

7 May, 2010 at 6:32 pm

AnonymousRicochet Robots is a good board game for multiple players involving figuring out how to move “robots” into certain squares on a grid given that they can only change direction when they hit walls. I only played it a couple of times but it was quite interesting.

7 May, 2010 at 7:37 pm

AnonymousOh yeah, also Chromatron at http://silverspaceship.com/chromatron. Use mirrors and eventually lots of other things to direct laser beams to the right places.

9 May, 2010 at 5:33 am

Erik ChristensenChess is a fine game that I play with my wife. I like also Sudoku, which is a very effective stimulant of brain functions (‘a sudoku a day keeps dementia away’). I have made a sudoku program, which you can see at my website. This program has many facilities and is very user-friendly. Best regards EC

9 May, 2010 at 7:34 am

YiweiIt could be interesting if someone designed some chess game for two players, so that the players may go through the textbook of linear algabra in the game (each step is definite) . I call this chess-encoding.

I recently consider to encode some math textbook into aerobics. If finished, one may learn math by dancing…

11 May, 2010 at 4:43 am

VinayakI remember reading this article by Douglas Hofstadter where he had described a game that had rules for changing its own rules. I forgot the name of the game though. Does anyone know what I am talking about?

11 May, 2010 at 7:25 am

Joshua ZelinskyVinayak, possibly Nomic?

11 May, 2010 at 10:46 am

EastwoodDCAt risk of repeating some that were previously mentioned, here is a short list of games which demonstrates some fundamental concepts that show up in many other games.

Nim – Demonstrates the first (last) move advantage.

Candyland – demonstrates Markoff chains.

Monopoly – is usually described as a Markoff chain, but can also be view as a Random Walk: http://giantbattlingrobots.blogspot.com/2009/01/random-walk-down-monopoly-lane.html

Cribbage – A fairly simple example of the basic point scoring framework. and can be thought of as a time-to-failure model (See Birnbaum-Saunder Distribution for metal fatigue). This same framework applies to just about every wargame/boardgame ever made.

Trivial Pursuit – demonstrates the geometric distribution (moving around) and negative binomial distribution (6 wedges + 1 to win).

Finally, and with apologies for “blowing my own horn”, this is a topic of particular interest to me. I’ve written about most of the games I mention above on my blog, and I’m always on the lookout for new ideas – And this thread has been absolutely packed with great ideas – Thanks Terence!

19 May, 2010 at 12:42 am

AnonymousHow about Beyond Waymark: http://www.octaspire.com/beyondwaymark/

Not an educational game, but extremely challenging and requires planning and logical thinking. Some of the levels, specially the later ones might take quite a long time to pass.

Contains also some quite challenging and unique(?) game objects like automatons that can/must be programmed by the player to carry out different tasks to change the structure of the level.

20 May, 2010 at 5:47 pm

PatrickSET is an awesome game that at least fosters mathematical thought processes even if one doesn’t actually approach it mathematically. There is an iPhone game called Thruple which is a one-player puzzler that is essentially the same mechanic.

Nurikabe and Sudoku are both heavy on logic. There are lots of Sudoku apps and a few Nurikabe apps (notably Nurikabe Vault).

Subway is a great set of logic puzzles on the iPhone.

Untangle Maniak is a Planarity app for the iPhone.

Math Zombie on the iPhone is great addition practice.

20 May, 2010 at 7:33 pm

PatrickOh, Colorbind is another great logic puzzle for the iPhone.

19 June, 2010 at 3:03 pm

capitanhookthere are lots of pysics games need math in flash websites

check out

20 June, 2010 at 4:56 am

AnonymousPortal

“http://store.steampowered.com/app/400/”

just the 2007 best game

24 June, 2010 at 7:52 am

David Snyderhttp://blackflip.org/

a good way to learn logic and goal-oriented reasoning.

20 July, 2010 at 4:38 am

gameshedI personally recommend Weapons Of Maths Destruction. It’s a flash game where the player have to destroy enemy tanks by answering simple math questions

17 January, 2011 at 2:33 am

GamesceFurthermore I think that most (normal) children will like Starcraft (2) much more than games like chess, draughts or go

17 January, 2011 at 2:33 am

haggleOh, Colorbind is another great logic puzzle for the iPhone.

17 January, 2011 at 9:49 am

Juan Miguel MontesI used to play a guessing game with my family for when we would go on trips, that we could play in the care / bus.

This is not a video game so I’m not sure if it qualifies as a game.

It is a very simple game, we take turns and whoever is “it” thinks of a product of prime numbers in his head – usually at least products of two digit prime numbers to begin with – and then tells everyone what product of two prime numbers he/she is thinking.

Everyone then tries to figure out the factors without using calculators or pen and paper, and the first person to guess the factors wins that round and gets to be the next “it”

So the challenge here is to mentally factor as quick as you can (yes my family is a bit nerdy).

It might not be a game for most kids itself, but me and my siblings and dad found it fun just for the quirkiness of it!

If it gets to be too easy then longer digit products of prime numbers can be said. I realize though that it doesn’t have the “crunch” factor that makes games addictive to play, because starting with smaller digit primes (say two digit primes) one quickly runs out of pairs to guess and three digit primes can be harder for most people to be enjoyable.

17 January, 2011 at 9:50 am

Juan Miguel Montessorry for typo, “…that we could play in the car/bus”

17 January, 2011 at 10:20 am

EastwoodDCJuan MM> This is not a video game so I’m not sure if it qualifies as a game.

“Video” is not required to make it a game. As far as promoting mathematical thinking goes, a video/computer aspect may not even be helpful.

19 January, 2011 at 11:06 am

science and mathPlaying number and math games with children help children to grow mathematical reasoning and increases interest in mathematics.

10 August, 2011 at 12:49 am

Niklas FI would really recommend Impasse.

http://www.bartbonte.com/portal/impasse.html

It really forces you to think ahead in discrete steps.

15 April, 2012 at 10:37 pm

jake wakCheck out spanish sites too…

http://www.frip.com

http://www.juegosdedisparosgratis.com

11 February, 2015 at 3:47 am

Pramod PonnaluriCheck out Three Sticks. It’s a highly creative and challenging board game that is based on geometry. http://igg.me/at/threesticks.

25 January, 2016 at 7:29 pm

60to5 (@60to5)New streamlined basic arithmetic online game. Check out http://60to5.com where you get 60 seconds to answer 5 questions. How far can you go?