First, we need to figure out which nine answers Julia heard from the other nine people in the room. Since the two people per couple already know each other, at most, any one person could have tapped elbows with eight other people (since they tapped elbows only with people they haven’t met).
Thus, since the nine answers are distinct from one another, Julia must have heard the answers: 0, 1, 2, 3, 4, 5, 6, 7, 8.
Now, how can we possibly figure out which is Florian’s answer?
Let’s start by calling the person who tapped eight elbows Person 8. It must be the case that Person 8 tapped everyone’s elbow except for Person 8’s own spouse (because they already know their spouse). Thus, everyone other than Person 8’s spouse tapped at least one elbow. Therefore, Person 8’s spouse must be the person who tapped zero elbows! So we now know Person 8 must be married to Person 0.
Now let’s consider Person 7. We know they didn’t tap Person 0’s elbow because, well, Person 0 didn’t tap any elbows. This means since Person 0 and Person 7’s spouse are out, Person 7 must have tapped elbows with all the seven other people.
Now, as before, this means those seven other people tapped elbows with at least two people (Person 8 and Person 7), which means the person who tapped elbows with only one person must be Person 7’s spouse. So we conclude Person 7 must be married to Person 1.
We can use similar logic to conclude Person 6 must be partnered with Person 2, and that Person 5 must be with Person 3. Finally, we get to the last remaining couple: One of them is Person 4, and the other has tapped elbows with Person 8, Person 7, Person 6, and Person 5—or, in other words, also four people. Thus, Person 4’s spouse is another Person 4.
Since Julia heard nine different answers, and didn’t hear two people answer that they had both tapped four elbows, it must be the case that Julia herself tapped four elbows. Furthermore, it also must be the case that Florian, her husband, is Person 4.
Thus, we have our answer: Florian tapped four elbows.
