On a table in the room stand seven bottles, along with a piece of paper inscribed with the following verses:
Danger lies before you, while safety lies behind,
First, however slyly the poison tries to hide
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:
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 second on the right
Are twins once you taste them, though different at first sight.
(Rowling 1998, p. 285)
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?
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.
1. Rick Jones | Kennett Square, Pennsylvania |
2. Kirstine Wynn | St. Olaf's College Northfield, Minnesota |
3. Whitney Wynn | Bellingham, Washington |
4. Richard K. Johnson | La Jolla, California |
5. Kyle Martin | North Andover, Massachussetts |
6. Guye Khandsuren | United World College of the Adriatic Duino, Italy |
7. Rodney Lenfant | Houston, Texas |
8. Danielle Alderman | Winchester, Virginia |
9. Frank H. Maire | Norwalk, Ohio |
10. Jeff Gaither | Winchester, Virginia |
11. Denu Voight | Winchester, Virginia |
12. Matt Stillwagon | Winchester, Virginia |
13. André Nielsen | Tullangen, Sweden |
14. Fredric Westholm | Örebro, Sweden |
15. Isabelle Groth | Sweden |
16. Emily Butler | Columbus, Georgia |
17. George Gaither | Winchester, Virginia |
18. Dan Bassett | North Andover, Massachussetts |
19. Evelyne Stalzer | Montville, New Jersey |
20. Carolin | Sweden |
21. Ashley Neumann | Winchester, Virginia |
22. Ronak Dixit | Columbus, Georgia |
23. Kerbey White | Winchester, Virginia |
24. Tove Westlund | Sweden |
25. Lina Öijerholm | Sweden |
26. Geoff Keith | Santa Monica, California |
27. Justin Curry | Harrisonburg, Virginia |
28. Katie Nickerson | North Andover, Massachussetts |
29. Chris Zetlin | Winchester, Virginia |
30. Kathleen Altemose | Winchester, Virginia |
31. Daniel Chronlund | Tullängsskolan, Örebro, Sweden |
32. Jimmy Careliussèn | Tullängen Örebro, Sweden |
33. Charlotta Österberg | Tullängen Örebro, Sweden |
34. Peggah Sadeghzadeh | Winchester, Virginia |
35. Tina Zahel | Winchester, Virginia |