Comment by anonporridge

The joke goes back to at least 1971 based on it's appearance in a book of Isaac Asimov's favorite jokes, https://old.reddit.com/r/KingkillerChronicle/comments/3uul26.... I'm sure it's much older. My father also told a version of it back in the 80s.

Screws and screwdrivers are at least 500 years old, so this joke could have been mutating around its core punchline through generations for quite a long time before it was first written down.