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It is my understanding that nouns with indefinite or no articles are negated with "kein" Example - Ich habe keinen Hunger

Why does "kein(en)" becomes "nicht" when we have another noun such as "Hitzefrei"?

As seen here: Warum haben wir nicht Hitzefrei?

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    Your second sample could be as well "Warum haben wir kein Hitzefrei". There's no such strict requirement as you claim. – πάντα ῥεῖ Apr 23 '18 at 17:09
  • But why is using "nicht" even acceptable here? Shouldn't it be wrong? – Evil Racehorse Apr 23 '18 at 17:37
  • "Shouldn't it be wrong?" Why should it? – πάντα ῥεῖ Apr 23 '18 at 17:55
  • Well, aren't nouns with no or indefinite articles supposed to be negated with "kein(e)" only? Or do we have complete freedom to use "nicht" and "kein" interchangeably? – Evil Racehorse Apr 23 '18 at 18:53
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    "Or do we have complete freedom to use "nicht" and "kein" interchangeably?" No, but there are exceptional and irregular cases as always – πάντα ῥεῖ Apr 23 '18 at 18:54
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In general "kein" is used with nouns, while "nicht" is used with verbs. Some examples stolen from Handout: Negation with Nicht and Kein:

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Since "Hunger" is a noun, the usual negation would be "kein", saying "Nicht Hunger haben" isn't grammatically incorrect, but quite unusual.

Though as always there are examples, where both negations could work well, but with different emphasis.

"Hitzefrei" is a noun as "Hunger" as well (and not even really translatable to english as a single word. The closest english translation I can think of is "a (school) day off due to an extraordinary heatwave").

The questions

Warum haben wir nicht Hitzefrei?

and

Warum haben wir kein Hitzefrei?

would work equally well.

An emphasis from context could be

Die Klasse 6a hat heute Hitzefrei.
Warum haben wir (Klasse 6b) nicht auch Hitzefrei?

In the above sentence emphasis is more on the verb (nicht haben) than onto the noun.

Though

Die Klasse 6a hat heute Hitzefrei.
Warum haben wir (Klasse 6b) kein Hitzefrei?

still would work equally well, but emphasis shifts slightly to the noun (kein Hitzefrei).

The english translations could be

Class 6a got a day off for the extraordinary heatwave.
Why did we (class 6b) not get a day off?

Class 6a got a day off for the extraordinary heatwave.
Why did we (class 6b) get no day off as well?

It seems that's bit of an exception / irregularity, and you can't really apply a strict grammar rule.

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