Answer to October 7, 2002 Problem by Roger Howe
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| The Harry Potter Problem |
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On a table in the room stand seven bottles, along with a piece
of paper inscribed with the following verses:
First, however slyly the poison tries to hide
Hermione, who is an exceptionally avid student,
realizes that she can use reasoning to determine
the bottles that they need to escape from the room.
As she says, "This isn't magic-it's logic-a puzzle.
A lot of the greatest wizards haven't got an ounce
of logic, they'd be stuck in here forever." Hermione thinks hard,
and in a few minutes she is able to identify the bottles that allow
escape. She goes back to sound the alarm, and Harry
goes forward to confront the evil-doer.
Can you figure out the contents of each of the seven bottles below,
just as Hermione did? |
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Solution to the Problem:
Bottles 1, 4, and 5 are poison. In the novel, you are not presented with a picture of the bottles and Hermione's reasoning is not explained. For a complete analysis of this problem, see Roger Howe's article in the February 2002 issue of the Mathematics Teacher. Faced with the lineup of bottles shown above, Hermione would have known from the third clue that neither the largest (giant), at position 2, nor the smallest (dwarf), at position 3, could be poison. From the fourth clue, she would then know that the bottle in position 6, that is, second from right, also is not poison. The fourth clue says that bottles 2 and 6 are the same, so they must be nettle wine. Thus, bottles 1 and 5 must be poison by the first clue. Two positions, positions 4 and 7, then remain as possible locations for the third bottle of poison. The second clue indicates that bottles 1 and 7 are different, so 7 is not poison and 4 must be. Bottles 3 and 7 are then the elixirs of escape. Since the second clue says that the end bottle, bottle 7, will not help move onward, it must be the potion for returning. Therefore, bottle 3 is the one to drink to continue the quest. |
