Hi everyone! I know this isn't exactly "math" but it is logic and you all are probably the most logical bunch on Answers. The riddle is as follows:
"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 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 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 the second on the right
Are twins once you taste them, though different at first sight."
NOW - there are a lot of websites which solve this puzzle but all of them do something quite annoying. They work backwards from Hermione's answer that the right most potion is the "move backward" potion and completely discount the clue about size. This website ( http://www.zhasea.com/logic/snape.html ) does however give a nice idea of the possible combinations. My exact question is - are there any other positions (where the move back potion is not on the right) for the large and small bottles that make the puzzle solvable? I have been looking at it for a while and I'm fairly certain that one still reaches the same possible configurations without Hermione's answer because any other positioning would make the puzzle unsolvable.
This is in the first novel and is not in the movies (I bet you forgot about the unconscious troll too http://harrypotter.wikia.com/wiki/Underground_Chambers#Fifth_obstacle)
"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 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 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 the second on the right
Are twins once you taste them, though different at first sight."
NOW - there are a lot of websites which solve this puzzle but all of them do something quite annoying. They work backwards from Hermione's answer that the right most potion is the "move backward" potion and completely discount the clue about size. This website ( http://www.zhasea.com/logic/snape.html ) does however give a nice idea of the possible combinations. My exact question is - are there any other positions (where the move back potion is not on the right) for the large and small bottles that make the puzzle solvable? I have been looking at it for a while and I'm fairly certain that one still reaches the same possible configurations without Hermione's answer because any other positioning would make the puzzle unsolvable.
This is in the first novel and is not in the movies (I bet you forgot about the unconscious troll too http://harrypotter.wikia.com/wiki/Underground_Chambers#Fifth_obstacle)