Ibraheem

florid fancies, and with a soul as fervent and imperious as his own.

  "When her lover turned and looked at her, and his eye met hers as she sat there, paler and whiter than any one in the vast ocean of anxious faces about her, he saw, by that power of quick perception which is given to those whose souls are one, that she knew behind which door crouched the tiger, and behind which stood the lady. He had expected her to know it."

This shows that what the princess points too it impacts the fate of her lover, this impacts all of the story.

And the princess hated her. She had seen, or at least thought she had seen, this beautiful lady looking at her lover with admiration.

This quote says that the princess has a characterization of jealousy and dose not like the lady.

she was the apple of his eye, and was loved by him above all humanity.

shes as barabaric and black and white as her father so she could go either way

Margaret

"He understood her nature, and his soul was assured that she would never rest until she had made plain to herself this thing, hidden to all other lookers-on, even to the king."

This means that he knew what he would choose deep down because of her nature.

This means that the princess was jealous, which would've affected her decision.

Think of it, fair reader, not as if the decision of the question depended upon yourself, but upon that hot-blooded, semi-barbaric princess, her soul at a white heat beneath the combined fires of despair and jealousy. She had lost him, but who should have him?

This shows that she is very in love and would pick the right door for him with the girl out

Jack

I think she led him to the door with the tiger because she did not like the girl and it would be better if he just died

And the princess hated her. She had seen, or at least thought she had seen, this beautiful lady looking at her lover with admiration.

I think the lady who told her which was wich switched doors so that the princesses lover whould die and so the princess would be sad and depressed.

this helps with the seduction of the guy for the answer

Bhargav

"And not only did she know in which room stood the lady ready to emerge, all blushing and radiant, should her door be opened, but she knew who the lady was. It was one of the fairest and loveliest of the damsels of the court who had been selected as the reward of the accused youth, should he be proved innocent of the crime of aspiring to one so far above him; and the princess hated her. Often had she seen, or imagined that she had seen, this fair creature throwing glances of admiration upon the person of her lover, and sometimes she thought these glances were perceived, and even returned. Now and then she had seen them talking together; it was but for a moment or two, but much can be said in a brief space; it may have been on most unimportant topics, but how could she know that? The girl was lovely, but she had dared to raise her eyes to the loved one of the princess; and, with all the intensity of the savage blood transmitted to her through long lines of wholly barbaric ancestors, she hated the woman who blushed and trembled behind that silent door."

this shows how much she hated the lady behind one door causing the uncertainty at the end of the text.

 "Would it not be better for him to die at once, and go to wait for her in the blessed regions of semi-barbaric futurity?"

This shows that the princess is making the decision of the fate of her lover based on what she wants to decide on and her intent.

As the youth advanced into the arena he turned, as the custom was, to bow to the king, but he did not think at all of that royal personage. His eyes were fixed upon the princess, who sat to the right of her father.

she would rather see him arring some one les than him died