Alice and Bill threw a party and invited four other couples. As each couple arrived there were greetings, including handshakes.
Later in the evening, Bill asked everyone, including Alice how many people they shook hand with. Every answer was different. No one shook hands with his or her own partner.
How many hands did Alice shake?
Alice shook hands with the 4 couples. Hence he shook 8 hands. Since hands are shaken at the greeting of a couple the number of hands shaken by another person would be less. Bill would have the same number of hand shakes as Alice but according to the question it seems the question is irrelevant to Bill because he asks others.