Harry Potter's metaproblem

Towards the end of Harry Potter and the Sorcerer's Stone, Harry and his friends encounter a logic problem. In the dangerous guarded passages below Hogwarts, they enter a room where magical fires spring up in front and behind. We are told that there are seven potions in a row, all different sizes, accompanied by the following doggerel:

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 this choice, we give you these clues four:
First, however slyly the poison tries to hide
You will always find some on the 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 on the left and the second on the right
Are twins once you taste them, though different at first sight.

Feel free to try to solve this, but you won't succeed. As in the book, the reader is missing crucial information: the placement of the largest and smallest bottles. The characters in the book, however, are not missing this information, and Hermione concludes that the smallest bottle contains the potion that will allow its drinker to advance through the flames unharmed. But even with this knowledge, the placement of the relevant potion is ambiguous to the reader.

But these questions can be answered:

Answers


Carl Muckenhoupt, Oct 27 2002