Pedro's Paradox
Here is an apparent paradox I first read about over 30 years ago. At the time
it seemed that there was no answer so the puzzle was forgotten
for about 20 years. Then one day it was rediscovered and I set
about solving it. Read carefully and give it some time. If you like,
you can download a pdf version
for easier printing.
Who Paid?
Pedro lived in a small house on the border of two countries, Garcia
and Marcia. These countries had enjoyed peaceful relations for
many years. There were no customs at the border, people could
travel freely between them and significantly one Garcian Dollar
had the same value as one Marcian Dollar. However things changed
as a result of a silly squabble between the two. Garcia decreed
that within its borders, a Marcian Dollar would be worth only
ninety Garcian cents. Marcia retaliated, so one Garcian Dollar
equalled ninety Marcian cents in Marcia.
One morning Pedro discovered that he was out of razor blades. (He
lived before the days of disposables!) Not only that, but also
his beloved razor had broken too. He decided to start his shopping
in Garcia, so he set off with ten Garcian Dollars in his pocket.
In Garcia he approached a shopkeeper and asked for a razor. "One
Garcian Dollar" he was told. He handed over his ten Garcian Dollar
note and was given a new razor and a ten Marcian Dollar note for
his change. This was correct, as it was worth only nine Garcian
Dollars.
Pedro still needed to buy some blades for his razor, so he decided
it would be best if he did that in Marcia. Without going home
first, he set off with his new razor and the ten Marcian Dollars
he received in Garcia. When he arrived, the shopkeeper was selling
razor blades for one Marcian Dollar. Paying with his ten Marcian
Dollar note, he received his blades and a ten Garcian Dollar note,
worth nine Marcian Dollars.
The paradox?
"Enough shopping for one day", thought Pedro as he returned home.
Tired but happy, he had bought what he wanted, but had ten Garcian
Dollars in his pocket just as when he started. Who paid for his
purchases?