Last week I had 3 flats in 24hrs. Specilized Armadillos stop a lot but not everything.
First - on the way home I picked up a short nail. I made it home without loosing air in the tire. It was at the edge of the tread and angle towards the sidewall. Hmm, maybe it didn't actually get the tube. Pulled it out with some pliers and Pewishhh. Nope, got the tube.
Second - next morning I was going down a side street in an area where people dump junk. The large pile of broken glass was hiden by all of the black plastic remains of a car fire, it was raining too. Tried to swerve but caught the edge of the pile. Front tire went down.
Third on the ride home, still raining, the rear went. I check my tires for glass after flatting and again at lunch time but I either missed a piece or picked up another one.

I usually have good luck with the dillo tires and a few I have worn down to the cords with no flats. I must have unknowingly killed a rat that day.