June 2012

# Age-old problem

If you take my advice, you should never ask a mathematician his age, or for that matter, the age of any of his family members.

This is what my friend, Ajit, faced when he wanted to know the ages of our mathematics teacher's three children. And before I tell you the whole incident, let me tell that Ajit is good at mathematics himself.

Well, one day Ajit had to visit the teacher's house on some errand. The teacher's three children were present there at that time.

"How old are they?" Ajit asked the teacher.

That was a mistake!

Without giving a straight-forward reply, the teacher said, "The product of their ages is 72. The sum of their ages is the same as my house number."

Ajit, as I told you, is good at mathematics. He felt that he had enough data to work out the ages of the three children.

Ajit stepped out to see what the house number was. After noting down the house number, he made some rapid calculations in his note-book, but drew a blank.

"That is insufficient data," he told the teacher, "I still can't tell."

"Okay, I will give you one more hint," the teacher said. This is the hint that the teacher provided, "My oldest child likes adventure sports."

Ajit scratched his head. How could a liking for adventure sports help him solve the problem. Can you help Ajit in determining the ages of the children?

• Union Public Service Commission - www.upsc.gov.in
• IIT-Kharagpur - www.iitkgp.ac.in
• Indian Statistical Institute - www.isical.ac.in
• Indian Institute of Technology Madras - www.iitm.ac.in
• Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
• Indian Institute of Mass Commission - www.iimc.nic.in
• IIT Bombay - www.iitb.ac.in