Which Alice?

Tweedledum or Tweedledee?
after, the other one came out bearing a sign, on the front of which
was written:
IS THE FIGURE ON
THE BACK OF THIS
SIGN A SQUARE?
The other brother answered by drawing a circle in the air.
Which one was Tweedledum?
WHAT QUESTION SHOULD ALICE ASK? "Congratulations, you
did it again!" both brothers cried.
"Now comes the best game of all, and if you win it, you also win a
prize!" said Tweedledee.
"This time," he continued, "we have not agreed which of us lies
and which tells the truth. What we do is this: we go into the house,
and each one comes out, each with either a red or a black card in his
pocket. Again, red signifies truth-telling and black signifies lying.
Now, just one of us has a prize in his other pocket. If you can guess
which one of us has the prize, you get it. It now is not important
which of us is Tweedledee and which is Tweedledum; your job is to
find out which one has the prize. Now, when we come out of the
house, you point to one of us and ask him a question—a question
answerable by yes or no. But instead of answering yes or no, he will
again answer in sign language: He will draw either a square or a
circle in the air. Now, the important point is this: if he is carrying
the prize, then by a square he means yes and by a circle he means
no. On the other hand, if he is not the one who is carrying the prize,
then by a square he means no and by a circle he means yes. On top
of that, he might tell the truth or he might lie—this is determined
by whether he is carrying a red card or a black card."
"But what question am I supposed to ask him?" inquired Alice.
"Ah, that is for you to figure out!" he triumphantly replied.
"That's the hardest part of the game, and if you can figure out the
right question, you certainly deserve a prize."
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