The problem is not that of the princess, although she does have a problem which only increases the problem her lover, the courtier, is already struggling with. The problem is in the courtier's choosing the right door. He is really only concerned about avoiding getting killed by the tiger. If he gets the beautiful bride, that is all very well and good, but what he mainly doesn't want is to see that tiger coming out of the door. The princess knows which of the two chambers contains the hidden tiger, but she has to decide whether to let the courtier get killed by the tiger or to give him the right signal and then allow him to marry another woman. She gives her poor lover a tiny signal indicating that he should open the door on the right.
Without the slightest hesitation, he went to the door on the right and opened it.
We might say that the lover's problem is solved at this point, whether the lady or the tiger comes out. At least it is no longer a problem. The story ends here. The reader never knows what happened, although he does know that the problem has been solved. Did the princess direct him to the door that would get him killed or to the door that would get him married to another woman?
...she hated the woman who blushed and trembled behind that silent door.
The right thing for the priincess to do, of course, would be to direct her lover to the correct door. But did she? No one will ever know.
The chief problem or conflict in the short story "The Lady or the Tiger" concerns the trial of the princess' lover. The king has issued a decree that the young man must face his fate in the arena and choose one of the two doors. The princess, using her power and influence, has uncovered the secret of which door has the lady or the tiger, and she gives her lover a tiny signal in the arena for which door to choose. The only problem is that the princess cannot decide whether to let her lover get married to someone else, an idea which the princess loathes, or to let him get gobbled up by a ferocious tiger.