Ich erkläre keinem Mann das Problem.

Breakdown of Ich erkläre keinem Mann das Problem.

ich
I
der Mann
the man
kein
no, not any
das Problem
the problem
erklären
to explain

Questions & Answers about Ich erkläre keinem Mann das Problem.

Why is it keinem and not keinen or kein?
Mann is the indirect object here—the person receiving the explanation. In German, indirect objects take the Dative case. Because Mann is a masculine noun, the negative article kein gets the Dative masculine ending -em, making it keinem.
The English translation says "not explaining ... to a man". Where are the words for "not" and "to" in German?
German handles this differently! Instead of saying "not to a man", German says "to no man" using the negative article keinem. Also, the Dative case itself does the job of the English word "to", so you don't need an extra word for it. Therefore, keinem Mann translates as "to no man".
Why does keinem Mann come before das Problem? Can I swap them?
In German sentences, when you have two objects that are both regular nouns, the Dative object (usually the person, like keinem Mann) almost always comes before the Accusative object (usually the thing, like das Problem). Swapping them would sound very unnatural.
Why is das Problem not in the Dative case too?
das Problem is the direct object—it is the actual thing being explained. Direct objects take the Accusative case. Since Problem is a neuter noun, its Accusative article is das, which happens to look exactly the same as its dictionary (Nominative) form. Only the receiver of the explanation gets the Dative case.

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