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THIS OLD MAN

This old man, he played one. He played knick-knack on my thumb

With a knick knack, paddy-whack. Give the dog a bone; This old man came rolling home.
This old man, he played two. He played knick-knack on my shoe

With a knick knack, paddy-whack. Give the dog a bone; This old man came rolling home.
This old man, he played three. He played knick-knack on my knee

With a knick knack, paddy-whack. Give the dog a bone; This old man came rolling home.

This old man, he played four. He played knick-knack on my floor (or door)

With a knick knack, paddy-whack. Give the dog a bone; This old man came rolling home.

This old man, he played five. He played knick-knack on my hive

With a knick knack, paddy-whack. Give the dog a bone; This old man came rolling home.
This old man, he played six. He played knick-knack on my sticks

With a knick knack, paddy-whack. Give the dog a bone; This old man came rolling home.
This old man, he played seven. He played knick-knack up in heaven

With a knick knack, paddy-whack. Give the dog a bone; This old man came rolling home.

This old man, he played eight. He played knick-knack on my gate

With a knick knack, paddy-whack. Give the dog a bone; This old man came rolling home.
This old man, he played nine. He played knick-knack on my vine

With a knick knack, paddy-whack. Give the dog a bone; This old man came rolling home.

This old man, he played ten. He played knick-knack all over again

With a knick knack, paddy-whack. Give the dog a bone; This old man came rolling home.
Actually, the line is "Seven...up to Heaven," "Nine...all the time," and "Ten...once again."
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There are probably serveral different variations and I don't think we can say one is right and one is wrong. The words I learnt as a child were the same as the ones in anon's posting. I was always very puzzled by the vine part...
This old man he played one, he played knick knack on my thumb with a knick knack patty whack give the dog a bone, this old man came rolling home. This old man he played two, he played knick knack on my shoe with a knick knack patty whack give the dog a bone this old man came rolling home. This old man, he played 3, etc.

It was a fun way to teach children how to count to 10.
Maybe it was Mick, Mack, Paddywack as a double meaning. Irish, Scott, and British oppressor would match them perfectly if one was referring to a paddywack as the person beating up the Irishman. "This old man came rolling home" could just be an arrogant recognition of the slow but sure fall of the British empire within it's neighbors within the Celtic (FYI- pronounced:"Keltic" for all the ignoramouses) region.
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Stretching credulity a little.