Puzzle: In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?
Answer given: If the lily patch is covering the pond fully on day 48, and it's doubled in size that means you only have to go back one day to when it was covering half the pond. So on day 47, the lake is half full.
I have my doubts about the answer and I was wondering how to mathematically get to the answer.
Found in an article of the Daily Mail.
The answer is correct.
Suppose the pond size is $x$ lily.
On day $48$, the pond is full, there are $x$ lily.
On day $47$, the pond must be $\frac{x}{2}$ (so that it doubles on the very next day).
But that is exactly the meaning of being half full.
Hence half full on day $47$.