Problematic age
Two professors are travelling in a train. One asks the other,"What are the ages of your children." The other says that the sum of their ages is equal to his house number, he tells the professor the house number, further he says that he has 3 children. He also says that the product of their ages is 72. The second professor asks for more information. The first professor says that his eldest son has blue eyes. The professor then predicts the ages correctly. Find the age of the eldest son
The answer is 8.
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1 solution
Find all the triplets whose product is 72. You will observe that the sum of each triplet is different except for the triplets of 6,6,2 and 8,3,3. As the professor knows the house number, he should have predicted the ages immediately. But the fact that he doesnt, implies that 2 of the triplets have the same sum. Thus the ages are 6,6,2 or 8,3,3. When the professor says that the eldest son has blue eyes, it means that the professor does have an eldest son which is not the case in the 1st triplet. Thus the age of the eldest son is 8.