TITLE: One lily pad, doubling in size every day, covers a pond in 30 days. How long would it take eight lily pads to cover the pond?
QUESTION [12 upvotes]: A lily pad sits on a pond. It doubles in size every day. It takes 30
  days for it to cover the pond. If you start with 8 lily pads instead,
  how many days does it take to cover the pond?

I think that the answer is $27$, but I don't really think that makes sense intuitively. I think that, intuitively, the answer should be less than $30/4$ since it is increasing at an exponential rate.

REPLY [3 votes]: Answering the 'why is my intuition wrong?' aspect:
The key thing to remember here is not everything is linear. The unrealistic nature of the question isn't what makes it unintuitive. It's that we have a tendency to think things are linear, even when we know full well they are not.
The reasoning used seems to be 'if I start with twice as much, it must only take half as much time to get to the same end amount'. That's using linearity, and basic ideas of addition/multiplication. But exponential growth is very very much not like this.
There are other places this comes up in life: if you are speeding up then you cover most of the ground at the end; if you are saving for your pension, a large part of your savings comes from the last few years (when your salary is highest); twins newly separated are only half the size of a single baby the same age, but they'll only take minutes longer to reach full size, not twice as long.