Like taking candy from a baby...

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"Who Shot Mr Burns? Part One” first aired in the US on the 21st of May, 1995. It was the 25th and final episode of Season 6. It is the only two-part episode of the show to date.

The concept of this episode first originated as a parody of the “A House Divided” episode of the 1960s television show, Dallas. The “A House Divided” episode of Dallas is more commonly referred to by fans as “Who Shot J.R?”, and famously involved a cliff hanger ending when the viewers had to wait until the following season’s premiere to find out which character had shot the show’s villain, J.R. Ewing.

Part One involves Springfield Elementary School accidentally striking oil while trying to bury a dead gerbil. This leads to the townspeople offering their ideas on how to spend the resultant money.
After (unsuccessfully) posing as a student to trick Principal Skinner into giving him the money, Mr Burns becomes overcome with greed and decides to tap the oil well himself, drying up the school's supply and forcing them to fire several employees. The resulting chaos sees almost everyone in town develop a reason to hate Burns.
At the end of the episode, Mr Burns (drunken with power after blocking out the town's sunlight) is walking away from city hall when he is "ambushed" by an unknown suspect. The episode ends with Burns collapsing onto the sundial, and several townspeople gathering around in shock.

Part Two examines several suspects and their motives. Originally, Smithers believes he may have shot Burns in a drunken stupor, but his innocence is later proven by a testimony from Jasper, the old man with a wooden leg (which is what Smithers actually shot.).
Lisa, trying desperately to clear Homer's name (after he is wrongfully arrested for the crime), makes it her mission to find the true shooter. With the help of the police, several suspects are eliminated including Tito Puente, Moe Szyslak, Groundskeeper Willie and Principal Skinner.
Finally, Lisa figures out who the real shooter is. At the same time, Homer (dressed as a doctor) bursts into Burns' hospital room threatening to kill him, and while Homer shakes him vigorously, Burns regains his ability to speak and reveals the true story:
As he was walking away from the city hall, he walked past the Simpsons' car, where Maggie sat alone, licking a lollipop. Burns, licking his lips, decides he wants it, and utters the phrase, "I think you'd better drop it." During the resultant struggle over the candy, Burns' gun falls out of its holster and into Maggie's hands, shooting him.

The townsfolk conclude that the shooting was an accident, and that "No jury in the world is going to convict a baby...well, maybe Texas.", but the episode closes with Maggie's eyes darting back and forth suspiciously, indicating that there may have been more to the story after all.