Hermione's Potion Puzzle

In the book "Harry Potter and the Sorcerer's Stone", Hermione Granger is locked in a room (in which she would like to go forward from) with 7 goblets and this riddle: - 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. -There are also these pieces of evidence found after Hermione solved the riddle: - The smallest bottle contains the Forward Potion- - "Which bottle will take you back through the purple flames?". Hermione pointed at a rounded bottle at the end of the line. The book never gives us the sizes of the goblets. Is it possible for the reader to find the position of all 7 goblets without knowing the sizes?