Answers to the Logic Puzzle-I

A gentleman was trying to tease a mathematician. He wanted to find out if the mathematician really knew anything. So he decided to give a puzzle the mathematician to test his knowledge.

He asked the mathematician to identify the ages of his three daughters. He gave him the following information.
1. The product of their ages is 36

The mathematician was unable to find the answer. So the gentleman gave him one more clue.
2. The sum of their ages is today’s date.

The mathematician was still unable to find the daughter’s age. So the gentleman gave him one more clue:
3. The youngest daughter has blue eyes.

The mathematician smiled and gave the answer.

Can you find the ages of the three daughters and also why the mathematician failed to give the answer after the second clue?
Also the third clue seems irrelevant but it still enabled the mathematician to give the answer. How and why?

Answer
The possibilities of getting the product of 3 nos. 36 are as follows:
• 36*1*1
• 18*2*1
• 9*4*1
• 6*6*1
• 6*3*2
• 9*2*2
• 12*3*1

The sum of their ages is today’s date:

• 36+1+1 =38
• 18+2+1=21
• 9+4+1=21
• 6+6+1=13
• 6+3+2=11
• 9+2+2=13
• 12+3+1=16

It would have been possible to get the ages if the sum of two combinations would not have been the same (13) since the mathematician knew that day’s date.
So when the third clue that the youngest one has blue eyes was given the mathematician got the answer. Reason there can be only one youngest daughter. Hence the answer (6, 6, 1)
So mathematicians do have logic was proved once again 