How Hermione deduced like this

How Hermione deduced like this from the words from a roll of paper?

Based on Hermione's deductions, from left to right, the potions lineup is:
1. Poison
2. Nettle wine
3. Potion to move the drinker forward through black flames
4. Poison
5. Poison
6. Nettle wine

****
They stepped over the threshold, and immediately a fire sprang up behind them in the doorway. It wasn't ordinary fire either; it was purple. At the same instant, black flames shot up in the doorway leading onward. They were trapped.
"Look!" Hermione seized a roll of paper lying next to the bottles. Harry looked over her shoulder to read it:

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 at first sight.

Hermione let out a great sigh and Harry, amazed, saw that she was smiling, the very last thing he felt like doing.
"Brilliant," said Hermione. "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."
"But so will we, won't we?"
"Of course not," said Hermione. "Everything we need is here on this paper. Seven bottles: three are poison; two are wine; one will get us safely through the black fire, and one will get us back through the purple."
"But how do we know which to drink?"
"Give me a minute."
Hermione read the paper several times. Then she walked up and down the line of bottles, muttering to herself and pointing at them. At last, she clapped her hands.
"Got it," she said. "The smallest bottle will get us through the black fire -- toward the Stone."
Harry looked at the tiny bottle.
"There's only enough there for one of us," he said. "That's hardly one swallow."
They looked at each other.
"Which one will get you back through the purple flames?"
Hermione pointed at a rounded bottle at the right end of the line.
"You drink that," said Harry. "No, listen, get back and get Ron. Grab brooms from the flying- key room, they'll get you out of the trapdoor and past Fluffy -- go straight to the owlery and send Hedwig to Dumbledore, we need him. I might be able to hold Snape off for a while, but I'm no match for him, really."
"But Harry -- what if You-Know-Who's with him?"
"Well -- I was lucky once, wasn't I?" said Harry, pointing at his scar.
"I might get lucky again."