Which Alice?

ALICE IN PUZZLE-LAND
will draw either a square or a circle in the air. One of those two
figures means yes and the other means no, but you will not be told
which figure means what. However, the figure which does mean yes
is already drawn on the back of the sign, but you will not be allowed
to see it until after you have guessed which of us is Tweedledee and
which is Tweedledum. The first brother (the one who answers the
question) will, of course, have already seen the back of the sign, so
he will know which of the square and circle means yes and which
means no. However, he might lie when he gives his answer in sign
language."
"I'm not sure I understand that," said Alice.
"Well, if, for example, the circle means yes, and the correct
answer to the question is yes, then if he tells the truth, he will draw a
circle in the air; if he lies, he will draw a square in the air."
"Oh, I understand!" said Alice.
"Good! Then we'll play the first game. One last thing: My brother
and I have already agreed that if Tweedledee answers the question,
he will lie, and if Tweedledum answers, he will tell the truth.
WHO IS WHO? The brothers then went into the house. Almost
immediately, one of them came out and stood in silence. Shortly
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