This is quite an old puzzle, but none the worse for that. Several followers might not know it.
In a remote jungle location there is a remarkable pond that is exactly circular. Even more remarkable is the water lily that grows every year in this pond. It springs up in the exact centre of the pond, and then doubles in size every day, until after 23 days it covers the entire pond. At this point it dies back and sinks, and is not seen again until the following year.
The question is: after how many days does the lily cover half the area of the pond?
Well, if the water lily doubles in size every day it must have covered half the pond the day before it covered the whole pond. So the answer is 22 days.