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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.

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marked as duplicate by Vikram, carmichael561, Lord Shark the Unknown, Bram28, Henning Makholm Oct 12 '17 at 3:58

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  • $\begingroup$ It is correct, think of lily growth as gp with common factor 2 $\endgroup$ – avz2611 Oct 12 '17 at 3:40
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    $\begingroup$ This question is very similar: math.stackexchange.com/questions/2429872/… $\endgroup$ – carmichael561 Oct 12 '17 at 3:40
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    $\begingroup$ One of the rare occasions that the Daily Mail gets something right! $\endgroup$ – Lord Shark the Unknown Oct 12 '17 at 3:46
  • $\begingroup$ @LordSharktheUnknown: Except they seem to have gotten the concept of an "IQ test" quite thoroughly wrong. $\endgroup$ – Henning Makholm Oct 12 '17 at 4:01
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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 $47$.

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