Origin of phrase "open-and-shut" as in "it's not an open-and-shut case"

Solution 1:

From the Online Etymology Dictionary:

Open-and-shut "simple, straightforward" first recorded 1841 in New Orleans.

No further information on the origin of this phrase is available from the other sources I checked.

Open-and-shut is certainly used in the positive sense. In fact, open-and-shut case is a common expression. Two examples:

• An Open-and-Shut Issue on Cruise Ships
• An open-and-shut case
• Golf's host clubs have open-and-shut policies on discrimination

And I also discovered that this phrase (open-and-shut) is extremely popular in golfing circles (think Open) with the hyphens dropped (open and shut or Open and shut). Examples (headlines):

• Some Open and shut Rules cases
• The Open and shut case: Louis Oosthuizen shows the charm of a front-runner...
• It’s an Open and shut case for Gallo
• The gospel according to Gulbis: Open and shut
• Woods wins first Open and Shut Championship