The game, and its rhyme, is fairly old, and widely known in UK, Ireland, U. S., etc.

1849, Gentleman's Magazine
How many miles to Hebron ?
Three score and ten.
Shall I be there by midnight ?
Yes, and back again.
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How many miles to Banbury Cross?
Three score and ten.
Shall we get there by midnight?
Yes, if you run well.
Then open your gates as wide as the sky,
And let King Georger and his men pass by.
It is so dark we cannot see, so thread the needle, Nancy,
One, two, three.
Warwick; from Alice B. Gomme, 1894-1898, vol. 1, (1984 ed.), The Traditional Games of England, Scotland and Ireland, Thames and Hudson.