[SOLVED] John and Mary go to Dinner Hi, I have this homework problem and so am posting it alongwith my suggested solution: Problem Statement: John and Mary are Married. They agree to go to dinner with four other married couples. so there are 5 couples, or 10 people altogether. They arrive at the restaurant, and because there are some people who do not know other people, there are some handshakes that take place and some introductions. Anyone who does not know anybody will shake hands with that person. People will not shake hands with someone they already know and ofcourse, you do not shake hands with your own spouse. At the end of the dinner, John asks all the people present, including his own wife, how many hands each of them shook. He gets the following answers 0,1,2,3,4,5,6,7 and 8. There are 9 other people there, and they give him 9 different answers. How many hands did John's wife Mary shake? Prove your answer My attempted solution: Out of a total of 10 people, Johns wife would not shake hands with herself and her spouse, in this case John. Hence she would have shook hands with 10 -2 = 8 people.