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→Analysis: bring the working of the logic puzzle into the main text |
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Dòng 16:
It was mentioned earlier that certain staff and teachers provided the protection for the Stone. In order, that would be: Hagrid (Fluffy), [[Muggles' Guide to Harry Potter/Characters/Pomona Sprout|Professor Sprout]] (Devil's Snare), [[Muggles' Guide to Harry Potter/Characters/Filius Flitwick|Professor Flitwick]] (charmed keys), Professor McGonagall (wizard chess set), [[Muggles' Guide to Harry Potter/Characters/Professor Quirrell|Professor Quirrell]] (troll), and Professor Snape (potions for the logic puzzle). While we have been told that Professor Dumbledore has also provided protection, the form his magic will take is unseen yet.
The logic puzzle Hermione solves is interesting, in that we see the question, and the solution, but not the initial setup. The solution, as determined by Hermione, is that the smallest bottle will move you forward, and the one at the right end of the line will take you back. Clearly, from the arrangement of the bottles and the associated clues, it is possible for Hermione to determine which potion is which. Is it possible, from the clues and Hermione's solution, to work backwards and determine what the arrangement must have been? In fact, it does not, as the third clue is based on the bottles' sizes, which we are not told; however, it does refine it to one of two possible setups, which either is uniquely solvable from the clues provided. A discussion of this puzzle, and the possible solutions, appears on the Discussion page for this chapter.▼
Neville's opposing the Trio is the first occasion where we have seen him evince any bravery whatsoever. Until now, he has seemed ineffectual, very weak magically, and at the mercy of the passing scene. It certainly seemed questionable as to just why the [[Muggles' Guide to Harry Potter/Characters/Sorting Hat|Sorting Hat]] placed him in Gryffindor. But the Hat apparently detected traits within him that, here, we see for the first time when he stands up against opposition; futilely, to be sure, but he is fighting to protect his House from losing more points due to the Trio's actions. This chapter marks a milestone in Neville's maturation, and his bravery is becoming more overt. Whether or not his magical ability can also progress remains to be seen, however.
=== Logic puzzle ===
▲The logic puzzle Hermione solves is interesting, in that we see the question, and the solution, but not the initial setup. The solution, as determined by Hermione, is that the smallest bottle will move you forward, and the one at the right end of the line will take you back. Clearly, from the arrangement of the bottles and the associated clues, it is possible for Hermione to determine which potion is which. Is it possible, from the clues and Hermione's solution, to work backwards and determine what the arrangement must have been? In fact, it does not, as the third clue is based on the bottles' sizes, which we are not told; however, it does refine it to one of two possible setups, both of which
There are seven differently-shaped bottles on the table in front of them, and the puzzle text is:
''Danger lies before you, while safety lies behind,''<br/>
''Two of us will help you, whichever you would find.''<br/>
''One among us seven will let you move ahead,''<br/>
''Another will transport the drinker back instead.''<br/>
''Two among our number hold only nettle wine,''<br/>
''Three of us are killers, waiting hidden in line.''<br/>
''Choose, unless you wish to stay here forevermore,''<br/>
''To help you in this choice we give you these clues four:''<br/>
''First, however slyly the poison tries to hide,''<br/>
''You will always find some on nettle wine's left side;''<br/>
''Second, different are those who stand at either end,''<br/>
''But if you would move onwards, neither is your friend;''<br/>
''Third, as you see clearly, all are different size,''<br/>
''Neither dwarf nor giant holds death in their insides;''<br/>
''Fourth, the second left and the second on the right,''<br/>
''Are twins once you taste them, though different at first sight.''
Is this enough to determine the initial arrangement of bottles? Let us say that B is the potion that allows you to go back, F is the potion that allows you to move forward, W is wine, and P is poison.
{| border=1
|From the Poem, we know that there are 3 P's, 2 W's, 1 B, and 1 F. Let us start blank.
|_ _ _ _ _ _ _
|-
|We know from Hermione's solution that B is the farthest to the right.
|_ _ _ _ _ _ B
|-
|From the 2nd clue, we learn that neither end can be F, so the furthest to the left must be B, W, or P. It cannot be W, since there is always Poison to Wine's left, from clue 1, and there is no spot to the left of the leftmost. As we know where B is already, we also know that it cannot be B. Therefore, it must be P.
|P _ _ _ _ _ B
|-
|Clue number 1 tells us that each of the two bottles of wine has poison to its left. If wine is not the second bottle, then we have the following choices for the remaining two P and the two W:
{| border=1
|P P W P W _ B || P P W _ P W B || P _ P W P W B
|}
Clue 4 rules out all of these choices, because in none of them does the sixth bottle match the second. So the second bottle must be wine.
|P W _ _ _ _ B
|-
|Now, we know that "''second left and second on the right''" are the same from clue number 4, so the second from the right must also be wine.
|P W _ _ _ W B
|-
|And now, apply clue number 1 again — poison to the left of the wine.
|P W _ _ P W B
|-
|At this point it becomes indeterminate as we can't see the sizes of the bottles to allow clue 3 to help us. The two solutions are equally likely, but whichever of the two is the "dwarf", the smallest of the lot, will be the Forward bottle, that being the only one not yet determined.
|P W F P P W B<br/>P W P F P W B
|}
Given this arrangement, we note that clue 3, "neither dwarf nor giant holds death," means that the giant must be one of the two wine bottles, as the Back potion is a smaller bottle, and the Forward potion is the smallest. This gives Hermione better than half of the puzzle already, as the giant must be either 2 or 6, meaning 2 and 6 must both be forward potion, back potion, or wine by clue 4, and as there is only one forward and one back potion in the set, both must be wine. So 2 and 6 are both wine, and 1 and 5 must be poison by clue 1.
As both wine bottles have been identified, and clue 2 says that 7 must be different from 1 but cannot be Forward, and we know that 1 is Poison, the only option available is that 7 is Back.
With three of the four non-poison bottles identified, and none of them the "dwarf" mentioned in clue 3, it is easy to determine that the smallest bottle must be Forward.
The analysis above assumes it is somehow possible to tell from which side the line of potion bottles is to be viewed since the definition of "left" and "right" depend it. From the written description of the room "... just a table with seven differently shaped bottles standing on it in a line," it is entirely possible the table was in the middle of the room and could be viewed from either side. However, Hermione "walked up and down the line of bottles" rather than around the table while contemplating the puzzle, which would suggest the bottles are only accessible from one side, as they would be if the table were pushed up against a wall. It is possible that Hermione simply assumed that the bottles were to be referred to only from the side of the room where she and Harry entered, and was staying always on that side of the table to ease her own thinking. It would, of course, be possible to affix the poem to the table so that the order of bottles is fixed relative to the poem; however, we are told that the riddle is on a scroll that Hermione can carry around. We have to assume some form of standard reference as to where the leftmost and rightmost bottles are, as the puzzle must be solvable. However, the fact remains that Hermione was lucky that the wizard who had already passed through had not made some trivial rearrangement of the bottles that would have invalidated the entire puzzle, and Harry was lucky that the same wizard had left any of the "go forward" potion for him.
== Questions ==
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