snape’s puzzle

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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 for evermore,
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 onwards, 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 atfirst sight.
JK Rowling, Harry Potter and the Philosopher;s Stone, from chapter 16,;Through the Trapdoor;.
Thefirst thing to realise is that the puzzle is different for us than for Hermione.Hermione can see which bottle is smallest and which bottle is largest, and we can;t.On the other hand, we know that the back bottle is at the right hand end of the line, and that the forward bottle is the smallest one, which, at the beginning, Hermione didn;t.We also know that Hermione was able to solve the puzzle, at least for the two important bottles, which means that the total information available to her is consistent with only one solution for those bottles.
For Hermione, the puzzle is to find out which bottles contain what.For us, it is to try to find out what the complete arrangement of potions was, and where the smallest and largest bottles were.It;s also possible that, if we can;t completely solve those, we can still find out where the forward potion was and what was in the largest bottle.
We also need to make a couple of reasonable assumptions about wha…