Floating Nose + Mate

[TimS]

Hello, I have a question about the following situation:

I'm lvl 9. My strength is 16.

It's my turn and I draw a "floating nose" (=lvl 10) from the door deck. Since I am about to win, another player plays the "Mate" card, which duplicates the "floating nose". Now I couldn't beat their combined strength of 20.

Since you can bribe the "floating nose" with an item worth 200 gold or more, I decided to bribe only the "Mate" card.

Does this leave me with just one lvl 10 floating nose now? Thus I could beat it and win the game?

Or do I have to bribe them both? (since when you are fleeing for example, you can only fight them all or flee them all, not flee one and fight one).

Let me know your thoughts.