I heard this from a friend who volunteers for the Missionaries of Charity. The MCs wear white saris, and over their saris are blue-striped veils that cover the head, gather on the shoulder, and sweep around the whole body down to the ankles-- see here, here, and here. I haven't quite ascertained the exact shape of these things. Putting them on seems slightly complicated, but the sisters told my friend that they do it quickly, in the dark, every morning.
But one day a couple of them needed to see a doctor. My friend took them in her car, and ended up in the exam room with them, where they had to take off the veils and put them back on afterwards. And they got all confused. It was light in the room and they could see what they were doing, which really threw them off!