MathDB

The exchange rate in a Funny-Money machine is

s

McLoonies for a Loonie or

\frac{1}{s}

Loonies for a McLoonie, where

s

is a positive real number. The number of coins returned is rounded off to the nearest integer. If it is exactly in between two integers, then it is rounded up to the greater integer.

(a)

Is it possible to achieve a one-time gain by changing some Loonies into McLoonies and changing all the McLoonies back to Loonies?

(b)

Assuming that the answer to

(a)

is "yes", is it possible to achieve multiple gains by repeating this procedure, changing all the coins in hand and back again each time?

Problem Statement