Apple core? Baltimore!

In a fine old Disney cartoon from 1952 called "Donald Applecore," Chip and Dale engage Donald it what appears to be an old childhood rhyme.

Details were sketchy on the web, but the idea is that when I finish my apple (having only a core), I say, "Apple core!" and you say, "Baltimore!" I then say, "Who's your friend?" and you say, "Him!" and point at some sap standing nearby whom I then pelt with said apple core. Donald, being a dope, says, "Me!" so they throw the apples at him. I love good old-fashioned angry Donald Duck.

I bring this up because it falls into that esteemed category of something I heard many years ago that has bugged the shit out of me ever since.