After reading the solution (not here, but where Cartalk gives their official solution) I filed this under “I wouldn’t have gotten this in a million years”.
Not only does this require a bizarre mathematical insight the average person wouldn’t get, they explain it in a way that doesn’t make it obvious at all how you would go about finding the solution.
I came up with 78, not 72.
Now I wonder how many correct answers to this they would have gotten. They never tally that up for us.