When I was in middle school, I remember once discussing with my friends different methods of counting with one's fingers, that is, assigning a numerical value to each finger so one could count the natural numbers up to a maximum number. For example, the configuration$\dots$ $$ \begin{array}{c|l l l l l} \text{Side\Finger} & \text{Pinky} & \text{Ring} & \text{Middle} & \text{Index} & \text{Thumb}\\ \hline \text{Left} & 1 & 1 & 1 & 1 & 5 \\ \text{Right} & 10 & 10 & 10 & 10 & 10 \end{array} $$ $\ldots$has a maximum number of $59$, and it is clear that one can represent every number between $1$ and $59$ using only one's fingers using this configuration.
My question is this:
What is the maximum number $M$ one can count to using only one's fingers, such that there exists a hand representation for each $n \in \mathbb{N}, n \leq M$? Also, why does this given configuration of numbers and fingers have a larger maximum than other configurations?
Unlike digital representations in base $n$, each number need not have a unique hand representation, although I suspect the correct answer will have a unique representation for each number.
I do not know the answer to this question and so don't truly expect a conclusive answer to be given any time soon, if at all.
Feel free to provide the best hand configuration that you could come up with, as well as any insights which may lead us all to the correct answer.
Thanks for reading and good luck!