I hope by now you guys know I'm nuts for discovery or inquiry learning. I truly, truly believe the adage "what you get out of literature depends upon the questions you ask it."
But beyond literature, curiosity and exploration and examination, I believe, lead to the "greater understandings" of Life. Wasn't it Socrates who said, "The unexamined life is not worth living"? Word.
Here's what you need to do:
Ask ONE question about some aspect of Hamlet.
No repeats, so read one another's questions. (cue evil laugh here)
Knowing how way leads onto way, it should be noted that a classmate's question can inspire your own question...just make note of it in your post. Perhaps these questions can lead us to what is so ambiguous, provocative, complex, and personally and emotionally challenging about this play.
So begin to wonder and ponder. Have fun & think hard!