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?
(In reply to re: solution
This is all well and good Charlie... ;-)
... but I/we were assured that this can be done without brute forcing/simulation/computer programming.
I look forward to seeing a practical way of doing this with pen and paper.