This is the 1823rd most frequent Polish word.
żadnego
"Żadnego" means "none" or "no" (in the context of negation, masculine or neuter singular genitive case).
In this sentence, 'żadnego' is used to negate the existence of ideas the speaker has, meaning 'not any'.
Nie mam żadnego pomysłu, jak to rozwiązać.
I have no idea how to solve it.
Here, 'żadnego' expresses the absence of any dog in the yard, emphasizing 'not a single one'.
Nie widziałem żadnego psa na podwórku.
I didn't see any dog in the yard.
In this instance, 'żadnego' is used to indicate the complete lack of problems, meaning 'none' at all.