## 2013-10-05

### Pyramid (exponential) Power (2)

Here is the answer of my math question.

### A1.

Assume the 3rd and 4th levels are complete, Hitoshi can get the money: 40^2 * 1000 * 0.25 * 0.9 - 1000 = 359000 Euro. Hitoshi is rich!

### A2.

Daniel is the same. Wait, Daniel needs the 6th level of the pyramid. To complete the 6th level, we need:

1+ 40 + 40^2 + 40^3 + 40^4 + 40^5 = 105025641 (around 100 million)> 2.5 million

There is not enough people in Berlin for Daniel. He lost his 1000 Euro every month. and Hitoshi lost Daniel as a friend. ;_;  Actually German population is around 80 million, so, even if all the German people joined this, Daniel can not get the expected full payment. Actually next answer shows Daniel has absolutely no chance to get any Euro.

### A3.

Hitoshi needs total 5 levels.

1+ 40 + 40^2 + 40^3 + 40^4 = 2625641 > 2.5 million

So Hitoshi's level needs a bit more than the people in Berlin. But if everyone is convinced in Berlin, even babies and children pay 1000 Euro every month, Hitoshi can be rich. (Which is basically impossible.) This also means Daniel has no chance to get any money.

A pyramid system is basically a Monarchy system. The king can get money and it is true someone is the king. So you can see the proof of someone gets the money. But I think the question is ``you'' can be a king or not. Well, good luck for that. I think if Hitoshi saw more than 30 people related with this system, Hitoshi has basically no chance in Berlin, Hitoshi is in the slave level in this case.

Essay question: Why do some pyramid systems try to expand to the foreign countries?