pull out of a hat

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pull something out of a hat

 and pull something out of thin air 
1. Lit. [for a magician] to make something, such as a live rabbit, seem to appear by pulling it out of a top hat or out of the air. He pulled a rabbit out of a hat and then pulled a chicken out of thin air.
2. Fig. to produce something seemingly out of nowhere. Where am I going to get the money? I can't just pull it out of a hat! I don't know where she found the book. She pulled it out of thin air, I guess.
See also: hat, of, out, pull

pull out of a hat

Produce suddenly and surprisingly, as if by magic. For example, We can't just pull the answers out of a hat. This expression alludes to the magician's trick of pulling some unexpected object out of a hat. That object is often a rabbit, and the expression pull a rabbit out of a hat is often used to mean "get magical results," as in Much as I would like to be able to pull a rabbit out of a hat, I doubt if I can find further funding for this project .
See also: hat, of, out, pull