Which Alice?

The Twelfth Question
"Oh, 1 wasn't counting that!" exclaimed Alice.
"You see, she can't count!" the Red Queen triumphantly exclaimed.
"Not a bit!" the White Queen agreed.
"You'll never be able to pass an examination unless you can
count!" said the Red Queen.
"But I can count," pleaded poor Alice. "It's just that I counted the
wrong thing!"
"That's no excuse," replied the Red Queen. "You should always
count everything, because everything counts."
Alice tried to puzzle this out, and the Red Queen continued,
"Now, here are the rules of the examination. We will ask you twelve
questions, and you are allowed at most three wrong answers in
order to pass."
And so the examination began.
THE FIRST QUESTION "Do you know how to divide?" asked
the Red Queen.
"Why, of course!" replied Alice.
"Very well then, suppose you divide eleven thousand eleven
hundred and eleven by three. What remainder do you get? You
may use this pencil and paper if you like."
Alice set to work and made a calculation.
"I get a remainder of two," replied Alice.
"Wrong!" exclaimed the Red Queen triumphantly. "You see, she
can't do division!"
"Not a bit!" agreed the White Queen.
Why don't you try this puzzle with pencil and paper, and see if
Alice was right? Then you better read the solution!
ANOTHER DIVISION "Let's try another division," said the Red
Queen. "How much is a million divided by a quarter?"
67