Which Alice?

ALICE IN PUZZLE-LAND
"Well," said Alice, "I'm afraid I can't do this without pencil and
paper, and I forgot to bring my memorandum book in this journey
into the Looking-Glass."
Tweedledee quickly went into the house and returned with a
pencil and a pad of paper.
"We'll be in the house while you are figuring out your question,
and when you are ready, call us and we will come out. Take as much
time as you like."
The brothers then went into the house, and Alice worked quite
hard on the puzzle. After a while, she shouted, "I'm ready." The
brothers then came out, Alice asked one of them a question, and he
replied by drawing either a square or a circle in the air. Alice
pointed to one of the two brothers and said, "You're the one who is
carrying the prize," and Alice was right.
How, in one question, could Alice find out which one has the
prize?
"Congratulations again!" said both brothers. "You have certainly
earned your prize!"
Alice was then given her prize, all nicely wrapped and tied
together. The more she tried unwrapping it, the tighter it got!
"Have you forgotten that you're in the Looking-Glass?" asked one
of the brothers.
"Oh, of course!" remembered Alice, who then tried wrapping it
and making the string tighter. This worked like magic; the parcel
almost immediately unwrapped itself.
The prize consisted of a pencil and a beautiful brand-new
memorandum book.
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