“ When we ask for any member of the Brandt family, every phone in South America rings.”

That sounds like the computer had a bad solution to “find a Brandt.”

The comment with the request to find this reference had me thinking it would be a single phone number misconfigured to call a large population.

It actually had nothing to do with a computer!

It was the luck of either Teela Brown, or Mr. Brandt depending on how you read the genetic trait of luck.

If you haven't read ringworld, you should. It's really quite good.

But stop before you get to ringworld's children or whatever it's called. Niven's furry fetish is in full force later in the series.