"Assuming we are counting quarter-twists."
I realize that there are people out there who like to count
half-twists as a single twist. I don't. I'm not trying to force my
way of counting twists on anyone. I always try to be carefull to make
this assumption explicit out of courtesy to those who might want to
count otherwise. (Sort of like the Axiom of Choice.)
In fact I DON'T know if that result is true if you count half-twists
as well. I suspect it is, but I don't have a proof.
You needn't jump up and down and point every time one of us
quarter-twisters reveals himself. This one, at least, is well aware
of his assumptions.