OK I will say at least this. THIS IS THE TOUGHEST RIDDLE I HAVE EVER FACED OF WITH. OH MAN, MY HEAD HURTS SO MUCH. Anyway........I just solved the riddle and it took me 50 minutes to think it over. Here's the answer....it's 4. Here, I will explain it to u too. It's given that every person shook hands with different number of people. That means at max one could've shaked with 8 people(Except himself and his wife). But that would also mean that there had to be someone who shook hands with no one. Let's call this person X. If I am correct(i believe I am) Only the spouse of the person who shook hands with 8 people could be person X. Now based on this principle I can also say that the spouse of the person who shook hands with 7 people, shook hands with 1 person. Now if I go on using this principle I will see that the host's wife shook hands with 4 people. I know my explanation is a bit crappy, but that's the best I can do now(my head hurts and I need to sleep). I will explain everything more clearly tomorrow (if u demand it and I beg u please don't).