10 finger puzzler

From a late-April (2022) podcast I think. I know the answer’s probably already been broadcast, but I’m still trying to figure it out. It depends on how complicated the finger positions you can accommodate. If any individual finger is either up or down, and no other possibilities, that makes the answer easy enough, closely related to several other Car Talk puzzlers. However Ray mentioned somebody like Spock (of Star Trek fame) might could come up with more combinations. Spock could move his fingers left/right in a coordinated way better than most people. Do you think I have to take into account the possibility of left/right finger movements too? This could be taken to extremes, painting dots on fingers etc.

Think base 2.

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It would have helped if you had given the puzzle.

Here’s the puzzle for those interested:

The statement of this puzzler is extremely simple. First of all, it is a non-automotive puzzler. It has nothing to do with cars. It is not a non-intellectual puzzler though.

The beauty of this puzzler really is its brevity.
It is elegant in its brevity and simplicity.

Here it is. In a nutshell, in all its glorious brevity.
You have 10 fingers, right? Five on each hand. Well, most of us have five on each hand. And you know that you can count to ten, but then I have to take my shoes off after that.

However, you can count to a much higher number using those 10 fingers and the question is, how high a number can you count to using those 10 fingers without any ambiguity or confusion? What I mean by that is, you can’t say well, if I take my index finger, raise it a quarter of the way up. That’s one. And another halfway up. That’s two, and three… That would be ambiguous and confusing and would obfuscate the true elegant nature of this puzzler.
Just using your fingers, to what number can you count?

A hint! This requires a certain amount of dexterity, one might say. Mr. Spock from Star Trek may find this easier to do than us humans.
I can do it, but I find it difficult. And that’s your hint. I think that’s a big hint!

My computer has 31 fingers of RAM bytes in it!

It’s just too mind numbing to think about. Problem is my fingers do not all work independent of each other. And some don’t go down half way without holding them. They worked 50 years ago so guess this is a young persons riddle. I’ll stick to a calculator.

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That implies I don’t have to worry about any finger position besides up/down. I think you are correct, and Ray was trying to say that in a subtle way, without totally giving away the answer.