This should be the correct answer.

I also found this formula ( r = (r - n - 1) / 2 ) looping until less than n
where n = number of names
...only I found that I didn't need to drop the fraction each iteration, I
could just do it at the end.

I like the easy-to-understand algorithm, but:
iterating over every number can't be performant
at the cpu level, this is doing 2 divisions, and 2 compares on each loop
plus an addition when the condition is met

https://twitter.com/jeffallen6767/status/850135769205227522