One of the students replied: “We have all been studying a whole number of years, the sum of our years of studying is equal to the number of years you have been teaching and the product of our years of studying is 180”.
“I’m sorry”, replied the Professor after some thought, “but that doesn’t give me enough information”.
“Yes, you’re right”, agrees another of the students. “But if we told you that one of us were into double figures in our years of study, then you could surely answer your question”.
How long had each of the four been studying ?