Puzzle #1

On a fine sunny afternoon at the zoo, a visitor was admiring the three giant tortoises snoozing in the sun. "Did you know that these tortoises can live up to 150 years?" asked a zookeeper.

"No," replied the visitor. "How old are these?"

"That would be too easy!" exclaimed the zookeeper. "How old are you?"

When the visitor told him, he thought for a moment, then said "The sum of their ages is four times your age, and the product of their ages is 3150."

The visitor went and sat down on a park bench, and calculated for a bit. Coming back to where the zookeeper was still puttering around, she said, "You didn't give me enough information."

"Well," said the zookeeper, "only one of the tortoises is older than you."

"Aha!" cried the visitor. "Then I know how old they are."

How old are the tortoises, and how old is the visitor?

Want a hint?

Think you know the answer? Send me email with your solution. You won't win anything, but if you like I'll add your name to the " List of People With Too Much Free Time".

Also, let me know how you arrived at the solution. My method was not particularly elegant (I did the brute force thing and wrote a computer program to check and reduce the possibilities...)

This puzzle is adapted from "Golumb's Puzzle Column Number 29: How Old Are the Turtles?" by Solomon W. Golomb, in the IEEE Information Theory Society Newsletter, Vol. 44 No. 4, December 1994. The mathematics are the same, the text is slightly modified.
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