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?
2007-05-26
21:04:25
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2 answers
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asked by
Scythian1950
7
in
Mathematics