You enterred college? How did you do that when you spell entered enterred?
Maybe he meant he was interred in college.
Some of the comments here definitely make me want to have some Vicks Vapor Rub handy to mask the stench.
Here I am going to give you an example. I have skipped levels in school many years ago. I jumped from tenth grade and enterred college concurrently. After almost two years of community college I could not go on. I transferred to a prestigous college and got two A grades somehow. I stopped since I was bored and wanted something better. During my Calculus studies when I receive an A grade I just remember taking an extra Calculus book in order to understand some of the principles. The problem was that I could not continue pass that because I was missing a building foundation in my math studies. I jump and skipped too many levels. So now I am able to study this huge concept yet I do not feel sure of where I stand. I did not have a firm foundation.
I understand that. Skipping grades, skipping certain concepts is possible. The so-called intelligent people can skip several levels while they climb the ladder of knowledge.
But in chess, no matter how much knowledge you may get to have, it always comes down to the specific position you're dealing with at a single point in time. One element changes and the previous 'secret' of that position may change into something quite unexpected.
Calculation is a must.
Wait, lol, no, I think it counts them 16! times
So (48!/32!) /16!
I'm a little too tired to think through this properly and I clearly don't remember exactly how it's done. Reasoning through only 2 and 3 pawns to check myself I think this is correct now though... final answer lol.
A simple problem ... how could every possible pawn formation be counted?
You have 48 choices for the first pawn, 47 for the second, and so on.
So I think it would be 48! / 32! which includes illegal positions. So you'd have to find a way to count illegal positions... good luck.
That is calculating. I specifically said I want to count them, not calculate them.
Yes yes, I long ago decided you are a troll (along with maybe half the other posters in this topic?)
But it was a fun question so I went ahead and responded to it... but not necessarily to you 
I don't care what the number is. I am trying to build a framework.
Like I said, building a framework--reducing the calculations--misses opportunities outside that very framework.
It both counts them and represents the logic behind the pattern of the counting.
You can use your fingers and reach the same number if you'd like.
The advantage of using your fingers is that you can one by one eliminate the illegal positions.
The disadvantage of counting one at a time is it will take (if I entered the numbers correctly) 71492 years if you count 1 position per second non-stop.
You enterred college? How did you do that when you spell entered enterred?
Probably by applying and being accepted.
Mathematicians are really clever in working out such problems. But still no answer for number of legal positions has been given. I think this is a harder question than you realize.
It can never be done, the number is way too astronomical. Without seeing all the possibilities, how can one say 'I've found the best move'? It's only best until the next refutation. We are operating in the dark.
Mathematicians are really clever in working out such problems. But still no answer for number of legal positions has been given. I think this is a harder question than you realize.
Some exponential number has been given. It would be bigger than the number of atoms in the Universe.
Mathematicians are really clever in working out such problems. But still no answer for number of legal positions has been given. I think this is a harder question than you realize.
Some exponential number has been given. It would be bigger than the number of atoms in the Universe.
The number of games exceeds the atoms in the observable universe. Total number of legal positions is more like the number of atoms in the earth. (But in both cases, the exact number is not known.)
If no number is known, how can one make a comparison? No one keeps counting as we speak, so that the number has exceeded those two, which are presumably known. And after that, a computer keeps counting...
You cannot form a framework unless the whole thing is seen. To form a framework based on what you currently see would be different than the framework built when the whole is seen.
If no number is known, how can one make a comparison?
Just like without knowing a person's exact height, you can tell whether or not they're shorter than a building.
In that case it's easy, you can measure them visually, and even there there are certain visual illusions. But here, some calculations had to be done and some numbers were arrived at.
Correct. They can set maximums and minimums without calculating the exact number.
For example, really easily, I can say the number of positions isn't greater than 64!/32! because that would contain illegal positions like both kings in check, or kings right beside each other. Already this is less than the estimated number of atoms in the observable universe.
I wonder how they estimated that number...
The way you deal with infinity depends on the context.
But yes, 1/9 = .1111...
2/9 = .2222...
3/9 = .3333...
etc
And 9/9 = 1
or .9999...