finger overflow!
(ten plus) one, (ten plus) two, ...
For base ten, you can just put a pebble down for each overflow, and the fingers will always count the units. If you were using base eleven, you would count [1,2,3,4,5,6,7,8,9,A],[10,11,12,13,14,15,16,17,18,19],[1A,20...], so a given finger wouldn't always correspond to the same digit.
If you were using base eleven you'd put your pebble down when you hit dec(11) aka base11(10). That pebble represents dec(11). Then first finger would be dec(12) aka base11(11) and once again your first finger represents 1.
So in base11 [1,2,3,4,5,6,7,8,9,A] - pebble - [11,12,13,14,15,16,17,18,19,1A]
A pebble and five fingers would be dec(16) instead of dec(15) but your five fingers still represent 5. The pebble represents 11 instead of 10.
But really, once you're into double digits you normally wouldn't be counting on your fingers anymore. You write 10.
I don't understand "[..] so a given finger wouldn't always correspond to the same digit."