immediately obvious upon consideration; easily decided: an open-and-shut case of murder.

1835–45, Americanism Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
easily decided or solved; obvious: an open-and-shut case

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Example sentences
It's not an open-and-shut case of creative borrowing, but the resemblance is striking.
Even then it would be far from an open-and-shut case.
While he sat there looking calm and flattered, he was an open-and-shut case.
It takes a good detective to put them all together and come up with an open-and-shut case.
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