Cookie Problem?

Question

A huge jar of cookies has N whole cookies. A cookie is drawn at random, broken into halves, of which one is eaten, the other tossed back into the jar. Subsequently, if any half cookie is drawn, it is eaten, if any whole cookie is drawn, it is broken into halves, etc. Eventually all the cookies are eaten. For large N, what is the number of whole cookies in the jar, and what is the number of half cookies in the jar, as continuous functions of half cookies eaten?

The "whole cookie" function starts with N, while the "half cookie function" starts with 1 (which we can approximate by 0), and both end in 0 after 2N half cookies are eaten. Bonus: At what point will there be a maximum number of half cookies in the jar?

Chewy chocolate chip cookies, because the dry ones crumble too easily when broken.

The CAT, I was looking for a functional description of what happens if, say, there was a billion cookies in that jar, so it's virtually a continuous function. Don't worry about the calories.

Answer 1

Mmmmmm, chewy chocolate chips!!!

You say the half Cookie function starts with 1
Maybe I'm totally off the cookie trail,
(have not done this in years...)
but here:


Cookies (n,1) = n/1 (n-1)

(n-1)*(n-2)/ (n-1) (n-0)

n^2-2n-n+2/n^2-n

n^2-3n+2/-n

-3n+2/-n

-2n+2

Or 2-2n

I don't think there was a very large number of cookies to start with...
I say there were only 2 cookies in that jar! (but maybe I'm wrong)

1) One whole and one half
2) Maximum number of half cookies in the jar would be 2.

But you had to eat them all!

Milk?

LOL, I'm not worried about the calories,since you ate the cookies!

But I would not know how to proceed for a billion cookies...

How could you eat a billion cookies anyways?

Think of the size of that jar!

How could you pick up the cookies in the bottom of such a jar?

Ladder?

How could you get that ladder in the jar without braking many-many cookies?

Oh, I forgot you are some kind of extra terrestrial locust, so your arms must be able to stretch all the way down.

Your arteries must be able to handle all the trans fats in those cookies!

How many chocolate chips are there in a billion chocolate chips cookies?

I just looked at my answer again and I think we are left with not zero cookies but minus two cookies!!

How can we be left with -2 cookies?

Where did they go?

But more important:

Where did these negative cookies come from?

Answer 2

are they Chocolate Chip or Oatmeal. Details man, Details