pull a rabbit out of the hat
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pull a rabbit out of (one's)/the hat
To do something surprising and seemingly impossible; to produce something in a way that has no obvious explanation, as if done by magic. A reference to the clichéd magician's trick of pulling a live rabbit out of a seemingly empty hat. The caterers really pulled a rabbit out of the hat by producing 100 cupcakes with just 20 minutes' notice. Unless someone can pull a rabbit out of their hat, I just don't see how we can fix the issue without starting the whole thing over again from scratch.
pull a rabbit out of the hatJOURNALISM
COMMON If someone pulls a rabbit out of the hat, they unexpectedly do something which solves a problem or helps them to achieve something. I cannot pull a rabbit out of a hat every time I go into the boxing ring. All I can do is do my best. Note: This expression is often varied. It looks as though I will have to pull a few rabbits from the hat. Almost every politician with whom they had dealings appeared to act as if rabbits could pop out of any hat. Note: You can also say that someone pulls something good or successful out of the hat. The Chancellor failed to pull any economic miracles out of the hat last night. He might still be able to pull something out of his hat, but I'd be kind of surprised at this point. Note: This expression refers to a traditional magician's trick, in which a rabbit is produced mysteriously out of an apparently empty hat.