I'd be going insane if this happened to me. I've had two flat tires in my entire life, not counting two schrader stems that blew out in the garage overnight because of a sharp-edged hole on a steel 27" rim (solved by switching to presta with a bushing).

Of those two, one was caused by a protruding spoke head and crappy rim tape in a cheap wheel and the other happened yesterday when the rain camoflaged our enormous post-winter potholes and I hit two in a row on 25c Ultra Sports. I think I might have pinch flatted on the first and hit the second with the tire flat already, in which case I'm VERY grateful (and surprised) that the rim isn't dented.

Clearly I don't ride enough miles.