Who sang knick knack paddy whack give the dog a bone?

I have no idea.

“This Old Man is a nursery rhyme of unknown origin. The rhyme and its associated tune have become well-known in popular culture through several renditions and parodies. Pete Seeger recorded this song in 1953.”

Source

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I would say it would have to be “That old man”

Only makes sense. The dog, bone, or paddywack could not make it up

I know Captain Kangaroo sang it once.

Here’s a famous parody by my favorite British parodists, Michael Flanders and Donald Swann. It’s called All Gall and it’s a satire of Charles de Gaulle sung to the tune of “This Old Man…”

“This old man, he played one,
He played knick-knack at Verdun.
Cognac, Armagnac, Burgundy and Beaune,
This old man came rolling home.

This old man, World War Two,
He told Churchill what to do,
Free French general, crosses of Lorraine,
He came rolling home again.

This old man, he played trois,
Vive la France, la France c’est moi!
Gimcrack governments, call me if you please:
Colombey les deux Eglises.”...etc.