Take off my skin and I won’t cry, but you will, What am I?

Answer: Onion

Solution:

I can run but not walk. Whereever I go, thought follows me close behind?

Answer: A nose.

Solution:

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A nose.

It is the great nemesis of the lactose intolerant.

Answer: dairy

Solution:

The more you have me the less you see. Shine a light on me and I flea. What am I?

Answer: Darkness

Solution:

Why are your nose and chin always at variance?

Answer: Because words are passing between them.

Solution:

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Because words are passing between them.

Its days are numbered.

Answer: calendar

Solution: