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:

- The Fibonacci version, 2584
- The 3D version
- The 4D version
- The really big version
- and more….

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?*

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