Thursday, July 13, 2006

Cryptonomicon and the Donut House

So I started reading Cryptonomicon, which is good so far. I only read it while going to the bathroom, so I figure it'll take a couple months to finish.

Early in the book, the main character is given an intelligence test for the Navy. The first question is about a 10 mph boat and a 5 mph river, and how long it'd take to get upstream or downstream 10 miles.

A-ha! It's a trick question. Some might assume that the boat would be able to take full advantage (or disadvantage) of the water's speed in either direction, but that's impossible, given the water's flow depending on distance from the shore, and also how it would travel through any bends in the river. He spent 2 hours proving a new theorem regarding that stuff, and they duly assigned him to play the glockenspiel in the band, since that's all anyone as dumb as him would be good for.

It reminded me of a question I saw a little while ago about a toroidal house. Three doors on the exterior wall, and three on the interior. They wanted to know if it was possible to start somewhere, go through each door once, and be where you started.

Obviously, there's more to the question, because the 3 doors on each wall precludes ever ending up on the same side of a wall after going through each one once. You can reduce that subproblem to walking through a door 3 times, and trying to end up on the same side. Trivial, and impossible.

But why did they say it was a house? Why not lines on a piece of paper with some non-trivial question about drawing more lines without picking the pencil up? A-ha! They want you to realize that since it's a house, you can climb over it without going through a door, and answer the question of whether or not you can go through all the doors once and end up on the other "outside." Then climb over and do it.

That problem is slightly less trivial, but doable, so the answer must be true! You can do it.

No comments: