Parental Advisory: This might cause your head to explode!
So I received one of those annoying chain mails today. After scrolling down the list of forwards and stupid one-liner comments like "oh well, usually I don't do this but " for a few minutes, I got down to the gist of it, and here's it:

"For every person you send this mail to, Bill Gates will pay you $245, for every person you've sent this mail to and who sends it to another person, he will pay you $244, and for each third person that receives this mail through the person you sent the mail to in the first place, Bill Gates will pay $243."

Now, it was obvious to me, that this was no different than any other of the 2379582394 generic chain mails that go around, but for some reason I wanted to find out exactly how many mails it would take to bankrupt Bill Gates if that mail's content was true. After a few hours of discussion and math explanation (my math sucks, big time!) with a friend from school, he had not only figured out a comparably easy formula (I was expecting a way more complicated one!) but had also managed to explain the formula to me in a way that my way-below-average understanding of math had been wrapped around it.
For example's sake, I will assume that every person receiving this email will forward it to another 10 people, who will then forward it to another 10 people and so on.
So it looks like this:

1. person sends 10 mails
2. persons sends 10 mails, resulting in 10x10 mails sent
3. persons sends 10 mails, resulting in 10x10x10 mails sent

thus it is true that the first person receives 10*245+100*244+1000*243 = 269850 Euro

Since every 2nd and 3rd persons who send that mail thus become a 1st person, as soon as their mail gets forwarded again, we have a nice loop here, which effectively, at least for a linear and easy way to calculate Bill Gates' bankruptcy, makes everyone in the chain a 1st person.
Considering the amounts of people I've seen in the recipients lists of those wretched chainmails so far (sometimes going beyond 50 recipients), I think I'm on the safe side when assuming that reaching 10 different persons on each level works even in today's situation of social networking...
According to Forbes Magazine, Bill Gates is worth $48 bil, which is roughly € 39,9 bil, which I will round up to 40 bil for calculations sake. Getting back to our calculation, while taking Billy's whopping net worth of € 40000000000, and our previously calculated € 269850 per first person, it would take this amount of emails (or different 1st persons) to bankrupt Bill Gates:

40000000000 / 269850 = 148230 (and a bit)

If you take the log_10 of that, you get the amount of levels it needs to get to that amount of emails (it is roughly 5.1).
It is safe to assume that Microsoft/Bill Gates would never go through with such a wild idea of wasting his money, ever.

The formula, for those who're interested in playing around with it, should be:

log_10 (b / (x₁*m + x₁*x₂*(m-1) + x₁*x₂*x₃*(m-2)) = n

with

• b = Bill Gates' networth
• x_n = amount of persons involved for payout (you could change this to x, y, z (etc) for distinction purposes)
• m = amount of money being paid
• n = levels required for bankruptcy

A boatload of thanks to Roland, who led me through this and worked out the formula. Thanks for wasting your time with me on a completely nonsensical calculation that serves no real purpose other than being posted on this blog. ;)

Ta-taa.