Wiktionary
open-and-shut
a. (context informal English) simple and obvious; easily decided alt. (context informal English) simple and obvious; easily decided
WordNet
open-and-shut
adj. so obvious as to be easily solved or decided; "an open-and-shut case"
Usage examples of "open-and-shut".
Should they ever refer to the actual content of the conversation, it would be the word of two career criminals with an open-and-shut murder charge hanging over their heads against the word of a police lieutenant.