Problem of the Week 902

Harry Potter's Bottles

Near the end of the book "Harry Potter and the Sorcerer's Stone", by J. K. Rowling, Hogwarts students Harry Potter and his friend Hermione Granger find themselves in a room with two doors. One door leads forward to a place they are trying to get to; the other leads back to where they have just come from, but both doorways are blocked by flames. In the room there is a table with a row of seven bottles on it, and the following note:

"Danger lies before you, while safety lies behind,
Two of us will help you, whichever you would find,
One among us seven will let you move ahead,
Another will transport the drinker back instead,
Two among our number hold only nettle wine,
Three of us are killers, waiting hidden in line.
Choose, unless you wish to stay here forevermore,
To help you in your choice, we give you these clues four:
First, however slyly the poison tries to hide
You will always find some on nettle wine's left side;
Second, different are those who stand at either end,
But if you would move onward, neither is your friend;
Third, as you see clearly, all are different size,
Neither dwarf nor giant holds death in their insides;
Fourth, the second left and the second on the right
Are twins once you taste them, though different at first sight."

Hermione studies the note and the row of bottles and comes to a definite, and correct, conclusion about which bottle will carry them forward and which will allow them to go back. What is the position of the bottle that allows them to move back?

Source: Suggested by Dan Velleman, Amherst College
© Copyright 2000 Stan Wagon. Reproduced with permission.

1 February 2000