So, thinking about how you would run this contest, you've got three basic ways of generating a random serial number.
The first is literally generating a random serial number; the problem being, there is an infinitesimal chance the serial number you just generated is in the pocket of someone in your listening area.
The second is to choose a sibling serial number of a bill in your pocket -- change one of the last couple of digits. If you're lucky, the sibling bills will have been delivered to the same bank in the same area and still be in circulation. But there's still a pretty slim chance it's even possible.
The best way to ensure that your contest is actually winnable, that your target bill is in circulation would be to start the contest by taking all the bills from your collective pockets, at the studio, writing down the serial numbers, and then handing them to someone to go buy coffee for the studio across the street. Wait a week or two, and your target bills will have circulated through the area enough, but almost certainly be in the pockets of people who could tune in and listen, and not someone halfway across the country.
So enter the 100,000 $1 bills sitting in stacks in this dude's house. Not circulating. At first, this isn't a problem -- he took out the bills after the contest start, after all -- but as time goes on, and the studio repeats the process of tagging and releasing new bills in circulation to generate new numbers to call out, suddenly, there is no chance that any of these hundred-thousand bills you are laboriously checking will work.