Visitors (1)/ were not permitted (2)/ entering the park (3)/ after dark. No error (4)

Answer

3

Explanation

to enter will replace entering because -
The to-Infinitive (Main Verb): functions as a Noun, as Adjective, or an Adverb.
In this sentence,
permitted to enter, to enter is the direct object, the Noun that receives the action of the Verb (Permitted).
To enter refers to a thing being done
or, desired to be done
Hence, to enter the park is the right usage