Miriam and I didn't think that we looked alike. But whenever Professor W handed back the homework in the course we took from him, there was a 50-50 chance that he'd hand me Miriam's homework, and hand her mine. We were the only female students in the class.
At first we exchanged homeworks discreetly so as not to embarrass W. Eventually we didn't bother, and would even walk across the room to trade papers. At some point W noticed and commented on it, but he never learned to tell the difference between us.
When I ran the above past Miriam, she replied "But there's more. That was back in the 70's. In the 80's I had a similar experience at work: there were just two female programmers, and we didn't look alike at all. Still, we were often addressed by each others' name. Things got better at my next two jobs, but only because I was the only woman programmer. I'd like to say things have improved since then, but then I saw this recent FaceBook post from [Harvard Computer Science Professor] Margo [Seltzer]."