The Cheshire Cat is a fictional cat appearing in Lewis Carroll's Alice in Wonderland. It appears and disappears at will, engaging Alice in amusing but sometimes vexing conversation. The cat often points out philosophical points that annoy Alice.

At one point, the cat disappeared gradually until nothing was left but its grin, prompting Alice to remark that she had often seen a cat without a grin but never a grin without a cat.

"Please, would you tell me," said Alice, a little timidly, ... "why your cat grins like that?"
"It's a Cheshire cat," said the Duchess, "and that's why."

The cat also uses logic to offer non-solutions to Alice's question:
"But I don't want to go among mad people," Alice remarked.
"Oh, you can't help that," said the Cat: "we're all mad here. I'm mad. You're mad."
"How do you know I'm mad?" said Alice.
"You must be," said the Cat, "or you wouldn't have come here."

Another example of this annoying practice is presented when Alice asks for directions:
"...thought Alice, and she went on. "Would you tell me, please, which way I ought to go from here?"
"That depends a good deal on where you want to get to," said the Cat.
"I don't much care where--" said Alice.
"Then it doesn't matter which way you go," said the Cat
"--so long as I get SOMEWHERE," Alice added as an explanation.
"Oh, you're sure to do that," said the Cat, "if you only walk long enough."

There are reports that Carroll found inspiration for the Cheshire Cat in a carving in a church in the village of Croft in the unitary authority of Warrington in the north west of England, where his father had been rector. The cat is named after Caroll's home county, Cheshire.

Brewer's Dictionary of Phrase and Fable says grinning like a Cheshire cat is "an old simile, popularized by Lewis Carrol". Brewer adds, "The phrase has never been satisfactorily accounted for, but it has been said that cheese was formerly sold in Cheshire moulded like a cat that looked as though it was grinning."

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