Each person could have shaken a maximum eight people, soon the nine people asked the ranges were 0 to 8. The person with 8 shakes must have shaken hands with those from 1-7 plus the professor. The person with 7 shakes must have shaken hands with those with 8, 6,5,4,3,2 plus the professor. Person with 6 shakes must have shaken hands with 8,7,5,4,3 and the professor. Person with 5 shakes most have shaken hands with 8,7,6, 4 and the professor. Person with 4 shake must have shaken hands with 8,7,6,5 only. Those with 0-3 shakes covered Above already.
