Die gefährliche Flotte soll hundert Kanonen gehabt haben.

From Lesson 422:Past hearsay (sollen)·German

Questions & Answers about Die gefährliche Flotte soll hundert Kanonen gehabt haben.

Why do we use soll ... gehabt haben instead of sollte ... haben?
sollte ... haben means "was supposed to have" (a past obligation or expectation). To express a current rumor about a past event ("is said to have had"), German uses the present tense soll paired with the perfect infinitive gehabt haben (past participle + infinitive auxiliary).
How is the perfect infinitive gehabt haben formed?
You form it by taking the past participle of the main verb (gehabt) and adding the infinitive of its auxiliary verb (haben or sein). Since the normal perfect tense of haben is "hat gehabt", its perfect infinitive is gehabt haben.
Why does the sentence say hundert Kanonen instead of einhundert Kanonen?
In German, when referring to exactly one hundred or one thousand, it is standard to drop the "ein" and simply say hundert or tausend. You usually only add ein- for emphasis or when it is part of a larger number like einhundertfünf (105).
If the rumor itself was in the past, how would this sentence change?
If people used to say the fleet had a hundred cannons, but they no longer do, you would change the modal verb to the past tense: Die gefährliche Flotte sollte hundert Kanonen gehabt haben.

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