Megan McArdle begins her excellent column thus:

There’s an old brain teaser that goes like this: You have a pond of a certain size, and upon that pond, a single lilypad. This particular species of lily pad reproduces once a day, so that on day two, you have two lily pads. On day three, you have four, and so on.

Now the teaser. “If it takes the lily pads 48 days to cover the pond completely, how long will it take for the pond to be covered halfway?”

The answer is 47 days. Moreover, at day 40, you’ll barely know the lily pads are there.