Two mathematicians met at a conference after a long time.
“So, how’s the family?”
“Very well! I have two kids now.”
“Really? How old are they?”
“Well, the sum of their ages is more than a quarter century, but neither is aged more than a score.”
“C’mon, you know I can’t guess based on that!”
“The product of their ages is a palindrome.”
“I am almost there, but you have to give me one more clue. Make it the final one, eh?”
“The difference between their ages is the tens digit of the elder one added to the age of the younger one.”
“Aah! I have it now!”
Can you guess the ages of the two children?