Season: 1
Air Date: 2/25/98

Cartman sets out to uncover his paternity and, as the title suggests, the mission is near impossible due to his mom being, quite literally, a dirty slut. The identity of his dad could literally be any of the various male supporting characters on the show, and not only did Matt Stone and Trey Parker leave the unbelievable reveal until the second season, they didn't reveal it until the second episode.