brain teaser help?

[Christopher lee]

Hi. Currently, you have 2 frogs. They double everyday. So it goes 2,4, 6, ... By the 30th day, at 2^30, they fill the pond. Now suppose you start with 8 frogs. They double everyday. How many days does it take to fill the pond?

I had, 2^30 = 8 * 2(n-1)
->n=28

but the answer is supposed to be 27. thanks!

 

[tostii]

You are basically starting on the 3rd day and the question is whether or not you are counting that day.

So, if you don't consider the starting day then n = 27, but if you do count the starting day then n = 28 makes sense to me.

 

[Gavin L]

\(2^{30} = 8 \times 2^k= 2^3 \times 2^k = 2^{3+k} \implies k = 27. \)

 

[Christopher lee]

does it make sense that using 8 as the starting point, I end up at 2^30 on the 28th day AKA 27days later? I think that's where i messedup

 

[tostii]

That makes sense. The question itself probably needs a little clarification.

"How many days does it take to fill the pond?"

If it is asking how many days later, your equation is wrong because it is counting the starting point 8 as 1 day later, which it is not.

 

[Christopher lee]

makess sense. thanks tostii

 

[CasanovaJ]

You know that this exact question (frogs and all) and its solution are in the Crack book, right?

 

[Anik Roy]

You know that this exact question (frogs and all) and its solution are in the Crack book, right?

What's a crack book, could you link me to it? Sorry I'm relatively new.

Oh woops. You mean Crack's book right? If so then I got it lol

 

[CasanovaJ]

What's a crack book, could you link me to it? Sorry I'm relatively new.

Oh woops. You mean Crack's book right? If so then I got it lol

http://www.amazon.com/Heard-Street-...0&sr=8-14&keywords=heard+on+the+street,+crack