A hair of the dog

Test No. [color=blue]incompl/inter-25 “Wrapped round her finger”, question 6

Well, unfortunately as I had one glass too many last night, I guess I should go for of the dog.

(a) a foot
(b) a hair
© a nose
(d) an ear

Test No. [color=blue]incompl/inter-25 “Wrapped round her finger”, answer 6

Well, unfortunately as I had one glass too many last night, I guess I should go for a hair of the dog.

Correct answer: (b) a hair

Your answer was: [color=green]correct
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where does this come from? I mean what’s the story? why hair of a dog?

Meaning: have another drink