Obfuscating True Elegance

Apr 30, 2022

Time for the new puzzler. I'm excited about this one. 

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!



How high can you count on just your fingers? We want to know the highest number you can count on your 10 fingers. And without any kind of ambiguity or confusion.
Just by holding up your 10 fingers.

We have the answer. It would be nice to have a video to explain this, but we are not that bright here at Car Talk! And we have always been told we have faces for radio, as they say! 
Okay, so here it is. The answer requires some dexterity. 

Hold up your hand with two closed fists, with the knuckles facing you, that is the number zero.
Raise the pinky on your right hand and that is the number 1. 
Lower that and raise your ring finger on the right hand and that is number 2.
The next number is number 3, and that's your pinky and your ring finger. 
Dr. Spock would have a good time with this!
The next number is number 4, and that is your middle finger, and the other fingers are down.

What I'm doing is I'm counting in Base 2!

Don't forget the question was how high can you count just using all 10 fingers. So Base 2 counting is each finger represents a number to the power of two.
So my index finger is two to the zero power, then two to the first power, then two to the second power, then to the third, fourth, fifth...And on and on like that.

And if I have 11 fingers, I can count to the number 1024.
But I have 10 fingers and therefore I can count one less than that, which is 1023.
And that is the highest number to which I can count is 512, plus 256, plus 128, plus 64, plus 32, plus, etc, etc...

Phew... That one was rough!


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