I lost the tip of one of my fingers when I was young, to a slamming door. It grew back itself, without any magic powders.

"Little pieces (16mm or so) are possible, but most of our wildest dreams about regenerating amputated body parts are still a long ways off."

I just had to measure it when I read that. Funnily enough, the mark that this wound left starts at about 15 to 17mm from the tip. I remember I lost my whole fingernail but somehow it grew back perfectly shaped.