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Monkey Business (Posted on 2004-04-30) Difficulty: 4 of 5
Suppose someone comes onto the site and is bored. That person starts spreading the rumor that levik is a monkey at exactly noon (on day 1) by sending an e-mail to one random person.

Then, each person sends an e-mail about this rumor (at exactly noon, on day 2) to one person. They can send it to anyone on perplexus (but themselves), even if that person already knows the rumor, or even if it was the person who told them about it.

Each successive day at noon, everyone that knows about the rumor sends a message to one other random person.

On average, on what day will everyone know about the rumor if there are 40 people (including the one that spread the rumor initially) at perplexus while the rumor is still spreading?

What if there were x people at perplexus while the rumor is still spreading?

No Solution Yet Submitted by Gamer    
Rating: 3.5000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Fibonacci's pet rabbits....... | Comment 7 of 11 |
(In reply to Fibonacci's pet rabbits....... by Penny)

Actually, while it may be somewhat based on Fibonacci's rabbits, this is a different puzzle altogether. The reason for that is the possibility of "misfires" (the person that Person X called today already had heard the rumor, so one less new person was added).

If there were no "misfires," then the day ("D") on which all M Flooblers had heard the rumor would always be the first day such that F(D)≥M (where F(n) is the nth Fibonacci number). In the case of 40 Flooblers, that would be 9 days [F(8)=34;F(9)=55].

But, because of the unknown (and increasing) number of misfires, it takes longer to exhaust the membership list.
  Posted by TomM on 2004-05-01 09:32:59

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