A curious student asks his math teacher: "I heard you have three daughters. How old are they?"
The math teacher says: "Well, the product of my daughters' ages is 72, and the sum of their ages is the number of the room we are in."
The student writes a few things down and then says: "I don't have enough information."
The math teacher exclaims: "Ah, of course! I forgot to tell you that my oldest daughter has green eyes."
The student says: "Oh, now it's clear. Their ages are..."
What are their ages?
There are 7 solutions.
The possible answers are:
The oldest daughter is 72 and the others are 1 and 1 and the room number is 74.
The oldest daughter is 36 and the others are 1 and 2 and the room number is 39.
The oldest daughter is 24 and the others are 1 and 3 and the room number is 28.
The oldest daughter is 18 and the others are 1 and 4 and the room number is 23.
The oldest daughter is 12 and the others are 2 and 3 and the room number is 17.
The oldest daughter is 12 and the others are 1 and 6 and the room number is 19.
The oldest daughter is 9 and the others are 1 and 8 and the room number is 18.
The first few solutions are laughable and unlikely, but all are possible.
Edwin