The woman stared at her. "That was an incredible feat of reasoning," she said at last. "You'd make a good witch finder." (2.16)
Even Miss Tick sees that Tiffany is a fast thinker right away. She has the kind of mind that performs well under pressure—she can think about things logically and thoroughly.
She walked forward, reading aloud about Garget of the Nostrils and the Staggers but keeping an eye on the ground. And there was another teddy bear, green this time and quite hard to see against the turf. (7.367)
The pictsies are expecting Tiffany to do some magic to find the doorway to Fairyland, and so she has to think quickly. She decides to read aloud from a book because they think that words are magical—what a clever girl.
If I was a world that didn't have enough reality to go around, Tiffany thought, then snow would be quite handy. It doesn't take a lot of effort. It's just white stuff. Everything looks white and simple. But I can make it complicated. I'm more real than this place. (8.198)
Even when she's in a frightening landscape, Tiffany thinks of ways that she could control the world and make it different. She knows that she has the agency and power to change things around her.
You're not very clever, thought Tiffany. You've never needed to be. You can get what you want just by dreaming it. You believe in your dreams, so you never have to think. (11.5)
The Queen may think that she's so smart and that she has the upper hand, but she's never had to actually think about things. She just creates dreams and traps people in them.
She thought she heard her brain creak with the effort of thinking. If she was in a dream, she had to wake up. But it was no use running. Dreams were full of running. But there was one direction that looked… thin, and white. (11.77)
The rules of this world don't really make sense, but Tiffany's going to find a way out of it anyway. She's got a mind that's constantly working to figure out loopholes and ways to triumph.
It had looked like a small drome in the trees. That meant it wasn't very powerful. She hoped so. She had to hope so… (11.139)
The dromes are something to avoid, but Tiffany runs toward one this time because she's figured out a way to hide from the Queen—she can hide out in a dream that she controls.
Tiffany couldn't think. Her head was full of hot, pink fog. It hadn't worked. Her Third Thoughts were somewhere in the fog, trying to make themselves heard. (13.5)
Once the Queen has got Tiffany cornered, she tries to impair her common sense and thoughts. Tiffany needs her brain to get her out of this mess pronto.
It's the Queen! yelled her Third Thoughts. It's her voice! It's like hypnotism! You've got to stop listening! (13.12)
Thankfully Tiffany's got her Third Thoughts on her side, which is just a fancy way of saying that Tiffany can think about what she's thinking about… which is really impressive for a nine-year-old.
"The secret is not to dream," she whispered. "The secret is to wake up. Waking up is harder. I have woken up and I am real." (13.152)
When she really thinks about what it means to be trapped in a dream, Tiffany realizes that she needs to wake up—and that once she wakes up, the Queen will no longer have any power over her.
"She'll be back then," said Rob Anybody. "She's awfu' stupid, that one. Clever with the dreaming, I'll grant ye, but not a brain in her heid." (14.6)
Even the pictsies, who the kelda said were not very bright, think that the Queen isn't actually that clever. She has some wicked dream powers, but she doesn't have the smarts to be a truly formidable opponent.