The recent viral hit game 2048 is one reason I have not posted in a little while. (The other factors are midterm grading for two classes and a great week-long research binge with a collaborator.) 2048 is a simple and hauntingly addictive game — you just move pieces left, right, up, down, until two 2s combine to 4, two 4s combine to 8, eight and eight are sixteen, sixteen and sixteen are thirty-two… Alright. Nostalgia over.
2048 is not the only such game. It was inspired by the game 1024 and is conceptually similar to Threes, neither of which I have played as I have a dumb phone. Part of 2048’s success is its very clean interface. But look at what it has spawned:
I started out by wondering what mathematics the game really contains. It looks like the game 1024 is a bit more consciously “educational,” but 2048 has the same mathematical content and more. What’s the content?
Addition: You don’t really need to know that 32+32=64 to play the game — you’ll learn soon enough so I would not call it a prerequisite. It might be a good way for kids to impress knowledge of powers of two into a personal mental list.
Strategy: I have a feeling that there’s some math in the combinatorics of the strategy. It’s a bit weird because of the random generation of tiles containing 2 and 4 — randomness isn’t something I usually consider in combinatorial games.
Pattern formation from random processes: I want someone to enlighten me about this. If you press only “down” and “left” with a few “right” buttons when you get stuck, you’ll usually get something that looks like a lower-right-antidiagonal matrix with an antidiagonal of 2s, an antidiagonal of 4s, and an antidiagonal of 8s (try it and see what I’m talking about). It’s clear why this happens — since you get random 2s and 4s, this method pushes everything down and right until it can’t go any further (a 4 gets nestled between an 8 to the right and an 8 below). But this has got to have some connections to more formal mathematics. In what other systems does this phenomenon occur?
Where/how else does math appear in 2048?
It is really cool that people have extended this to 3D and 4D versions: more mathematical layers start appearing and these are fun ways to get intuitive practice in spatial reasoning. The Fibonacci version also introduces people to some great number sequences!
How can we hijack the trend to do a little fun math ed?