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As I’ve noted before, Leo is fascinated by huge numbers. Tonight we were trying to figure out what Tree(3) means, and we got all into recursive graph representations. That was all a little too complex (even for me, a least in trying to explain it to a 7-year-old!), so I decided to try to flip the problem on its head. We created a game called…well, computer scientists would call it the Minimum Description Length game, but we just called it the Shortest Equation game.

You start with a pretty big number, say 748. The goal is to use any normal math operations that a 2nd grader would know (i.e., +-/*, powers and roots, !, and that sort of thing) to create the shortest equation that gets you to that number, using only single digit numbers (and allowing 10). So, you can’t just say, for example 748-=748, or 700+48, but need to break it down to single-digit numbers (and 10s).

Score each digit, and operation, including parens, as a character. (And we were a little fast and loose about whether you can rely upon order-of-operations, which I usually don’t like, and would rather it never be taught, but then you end up with a LOT of parens!) You can play against one another, or collaboratively.

Here’s our whiteboard after playing 748 for a few turns:

So, Leo started with (7*10*10)+(10*9)+8 for 18 characters, and we got all the way down to 8 chars with 3^3^2+10+9 (which doesn’t have the up-arrows if you use superscript notation…and notice that this is one place where we’re playing a little fast-and-loose with order of operations, so that we’re reading 3^3^2 as 3^27, whereas you could also read it as 9^2, so we really should have used two parens, but it’s still only 10 long! 🙂