A Professor asked four students how long each of them had been studying.

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 ?

The prime factors of 180 are 2,2,3,3,5 (their multiplication is 180). So we have 5 numbers, and we need to reduce them to 4. We know one of the guys studied for two figure number. So we have to use two of these numbers, to make a single 2 digit number.

It is either 5x2=10 OR 5x3=15

So possible solutions are

10,3,3,2 (total of 18 years)
15,3,2,2 (total of 22 years)

Chosing between the two needs some more information. The professor knows the answer, because he knows how long he has been teaching, but I do not really know.

Posted by arbor on 2003-04-30 11:51:12