MathDB

You live in an economy where all coins are of value

1/k

for some positive integer

k

(i.e.

1, 1/2, 1/3, \dots

). You just recently bought a coin exchanging machine, called the Cape Town Machine . For any integer

n > 1

, this machine can take in

n

of your coins of the same value, and return a coin of value equal to the sum of values of those coins (provided the coin returned is part of the economy). Given that the product of coins values that you have is

2015^{-1000}

, what is the maximum numbers of times you can use the machine over all possible starting sets of coins?
Proposed by Yang Liu

Problem Statement