Cherokee-Blackfoot Indian ?

I am about one-fourth cherokee, my dads dad was full blooded, and about one-sixteenth Blackfoot, my moms grandfather was full blooded, and there might be others somewhere along the way that I don't know. Is this wrong and is there a way to find out which reservations I am descended from, because I'm really interested in finding out more about my history. And also I've heard that this type of mixture Is impossible, is that true?