"I've always been 45 years older than your Dad", said Grandma to young grandson.

"But now the two digits in my age, both prime, are the reverse of the two in your Dad's age".

How old is Grandma?

For Grandma to be older than Dad the digits must be in descending order in her age, and ascending in Dad's.

Since Grandma is 45 years older than Dad, she can't be in her 20s or 30s. Nor can she be in her 50s, because then Dad couldn't even have a double digit age, leave alone sire a son of his own. (53-45=8 and 52-45=7).

So she must be in her 70s.

Since Grandma is in her 70s, Dad can't be in his 50s. Nor can he be in his 30s, because then Grandma's age would be overstated, and she would mind terribly. (35+45=80 and 37+45=82).

So he must be in his 20s.

Since the digits in their ages reverse, they must be 27 and 72.

Moreover, once we have removed the impossible, what remains, upon taking 27 from 72, however improbable, must be 45. No need to even check.

Eliminatory my dear. What son?

Posted by Sanjay on 2003-06-09 14:37:25