Using "um...zu" with past participle

Question

I want to connect these two sentences with "um...zu":

Wir sind nach Paris gefahren. Wir haben den Eiffelturm gesehen.

Before that, I was just connecting simple present sentences and it was more or less straightforward. But now I am a bit lost with past tense. I wrote it in this way:

Wir sind nach Paris gefahren, um den Eiffelturm zu sehen.

However, the answer in the video lesson says it is supposed to be like this without explaining why:

Wir sind nach Paris gefahren, um den Eiffelturm gesehen zu haben.

Are they both correct, why or why not?

Answer 1

They are both technically correct. Your answer, however, is the one that makes more sense in the context. The infinitive clause is final, i.e. it describes a purpose. Did you go to Paris in order to see the Eiffel Tower, or in order to have seen it? In my opinion, the former makes more sense. The latter is possible when thinking about a bucket list scenario where the goal is to cross something off.

Let's look another example where the contrast makes more sense:

Ich bin nach England gegangen, um in der Premier League zu spielen.
≅ weil ich in der Premier League spielen wollte

Ich bin nicht nach England gegangen, um mal dort gespielt zu haben.
≅ damit ich sagen kann, daß ich dort gespielt habe

With present tense in the main clause:

Man geht hin, um etwas zu tun.
≅ weil man etwas tun möchte

Man geht hin, um etwas getan zu haben.
≅ damit man das Gefühl hat, daß man etwas getan hat

In the above cases, the opposition between infinitive and infinitive perfect in a final infinitival clause with um … zu does not seem to be temporal: it seems to be between genuinely wanting to do something and doing something just for the sake of having done it, e.g. doing something merely in order to be able to claim or feel that one did something. Note that the infinitive perfect in these clauses is rare!

The following passage uses the contrast in order to characterise a type of person:

Ich befand mich eines Tages in einer Kunstausstellung Unter den Linden, in einer jener vielzuvielen Schaustellungen, die der Berliner Kulturmensch besucht, weniger um sie zu sehen, als um sie gesehen zu haben […] (Moszkowski, Der Venuspark: Google Books)

Answer 2

I see a slightly different emphasis lurking under the surface:

um den Eiffelturm zu sehen

means, you went to Paris, because you wanted to see the Eiffel tower.

um den Eiffelturm gesehen zu haben

There are two possible meanings I would assume with that phrase:

1. You wanted to be able to tell, that you saw it after returning from France (but already found it ugly from the pictures seen before)
2. You just wanted, to tick that mark on a places to be seen list