A bit complicated. I am learning Tabla, and my teacher counts to 16 on one hand; 3 finger segments plus the bit below the finger, for a total of 4 per finger. Starts from top of index finger and ends at bottom of pinky finger.
Thinking about my fingers while hitting something with my fingers might be a bit much for my brain! But actually it seems quite intuitive to layout a beat pattern that way. Thanks for prompting me to search what Tabla is, there is some great artists out there.
Actually, you don't do those things at the same time. The finger thing is mostly for clarifying the beat patterns before you start playing. On the Tabla, or actually in Northern Indian music, you do things like play a 27 beat bar and a 16 beat bar at the same time, and pseudo merging back on the 80th beat (16x4 and 27x3-1).
For a 5th position per finger you can add your fingernail. Count to 400 with both hands. Also has the nice property of 100 per finger on the second hand.
In this way, each bar is one finger.