I asked for help about a mathematics problem on M.SE and someone answered with a valid proof resorting to a reasoning I wouldn't have imagined, without giving details about how he got that idea.

Is there an adjective or a phrase that qualifies such a proof? To a more general extent, how do you qualify the outcome of an operation (of the mind, or something concrete) that is unexpected but still satisfactory?

There's a French phrase for it: sorti du chapeau.

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    In English, we do not use spaces before our question marks or our colons. – tchrist Feb 16 '14 at 18:38
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    Care to point to the math question? – bossylobster Feb 16 '14 at 22:44

You can pull something (sometimes a rabbit) out of a hat - that's the exact equivalent of your French idiom.

You can also produce something out of the blue, from nowhere, or out of thin air.

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