you can double that with every physical property you care to add.

fingers arent innately binary, you can curl them and point them.

wrist orientation relative to the hand and at that point you can count up to 2048 without resorting to too much more than a set of two rules (past instinctual counting)

Don't forget about birth defects. I went to school with a kid that was born without pinkies, but otherwise completely normal looking hands. You could still tell something was off when you looked at his hands, but it usually took a few seconds for it to register with most people.