You overhear a conversation between a professor and his teaching assistant. They are talking about a course they are running with just three students.

**Professor**: The product of the ages of the students in our class is 2450 and the sum of their ages is twice your age. Can you tell me how old they are?

**Assistant**: (After thinking for a little while) No.

**Professor**: I'll let you in on a secret. I am older than all of them, and now you can answer the question.

**Assistant**: (Even though he does not know how old the professor is, he thinks for a bit, smiles, and says) Yes I can.

Given that all of the ages involved are integers (whole numbers), how old is

*the professor*?

50

ReplyDeleteI learned from yesterday to keep in mind WHEN the person being questioned is capable of finding a solution to eliminate unique solutions.

So, I came up with a bunch of ways to factor 2450... but since the assistant clearly knows his own age, only two of those could be correct. 5 10 49 and 7 7 50. Both sum to 64 meaning that the assistant is 32.

I can eliminate 7 7 and 50 because the assistant was able to answer the question only after professor revealed that he was older than all of the students. If the professor were 51 or older, then both answers would be correct. So the professor must be 50.

So... The students are 5 10 and 49. The assistant is 32. And the professor is 50.

Right?

Right.

ReplyDeleteMy answer, which I wrote out yesterday, looks an awful lot like Ady's. So, I'll leave Ady's solution.