Tuesday, February 22, 2011

The Bottle Imp

The ‘Bottle Imp Paradox’ is similar to the Unexpected Hanging, but it's a fun one.

“You are offered the opportunity to buy, for whatever price you wish, a bottle containing a genie who will fulfill your every desire. The only catch is that the bottle must thereafter be resold for a price smaller than what you paid for it, or you will be condemned to live out the rest of your days in excruciating torment.

Obviously, no one would buy the bottle for 1¢ since he would have to give the bottle away, but no one would accept the bottle knowing he would be unable to get rid of it. No one would buy the bottle for 2¢ either: he would be unable to sell it since we just established that no one would take it for 1¢. Similarly, no one would buy it for 3¢, and so on. However, for some reasonably large amount, it will always be possible to find a next buyer, so the bottle will be bought.”