Which Alice?

Tweedledum or Tweedledee?
Alice's next adventure was far more pleasant. "I hate these
examinations," said Alice to herself, shortly after she had left the
company of the Queens. "They remind me so much of school!"
Just then Alice practically stumbled on Tweedledum and
Tweedledee, who were grinning under a tree right by their house.
Alice looked carefully at their collars to see which was marked
"Dum" and which was marked "Dee," but neither collar was
embroidered.
"I'm afraid I can't very well tell you apart without your embroidered
collars," remarked Alice.
"You'll have to use logic," said one of the brothers, giving the
other an affectionate hug. "We were expecting you to come around
these parts, and we have prepared some nice logic games for you.
Would you like to play?"
"What are the games?" asked Alice.
"Well, there are two games. The first is called Which of Us Is
Tweedledee and Which Is Tweedledum? The second is called
Which of Us Is Tweedledum and Which Is Tweedledee? Which
game would you like to play first?"
"They sound so horribly alike," replied Alice. "It's dreadfully
confusing!"
"Ah, they may sound alike," he replied, "but that doesn't mean
they are alike, nohow!"
"Contrariwise," replied the other, "if they were alike, they
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