Which Alice?

Which Alice?
"Which Alice do you think you are?" asked the King.
"At this point, I hardly know!" she replied.
"Are you of Type A or Type B?" asked the King.
"I'm afraid I don't know that either," replied Alice. "In fact, right
now I am not sure whether I am asleep or awake."
"Well, let me test you," said the King. "What color are your eyes?"
"Why, they're brown, of course— Oh, no, I think they're blue!
Now wait, it depends on which Alice I really am. Which Alice am I,
and what color are my eyes?"
"Well, let me put it this way," replied the King. "The Jabberwocky
happens to know about you and the other Alice. When he's asleep
he believes that one of you has brown eyes and that the other one
has blue eyes. When he's awake, he believes that you have brown
eyes and that the other Alice has blue eyes. Now can you tell me the
color of your eyes?"
Well, dear readers, I shall leave this little puzzle with you to solve
all on your own. What color eyes does my friend Alice have, and
what about the other Alice? A second problem: What type is the
Jabberwocky?
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