@NOOC
That's exactly why I wanted to make sure, that we are answering the same question.
So: What would you like to anwers?
1) All possible permutations? I think this was asked by CA, and that is what I answered for. The number of ways to distribute 64 pieces on a 8x8 square, irrespective if they match or not.
2) How many tries you maximally need to solve it? This is what I think you are talking about in your 3 last posts, but not in your first posts on page 1.
You stated yourself:
NooneOfConsequence wrote on Dec 6
th, 2019 at 2:50pm:
Now how many attempts you need to solve it is a different question
I go into that a little bit in the very last bit of my previous post: the extra mile. The "stupid method", which is a method to solve it, although stupid and tedious, yes, absolutely. But it gives an upper bound which is: not more than actual number of permutations or states.
I put in in there because you said:
NooneOfConsequence wrote on Dec 6
th, 2019 at 5:52pm:
The maximum number of states for an 8x8 puzzle is 16640.
but you also say:
NooneOfConsequence wrote on Dec 6
th, 2019 at 2:50pm:
The worst case for number of attempts is maybe in the hundreds of thousands, but way smaller than 8x(64x63x62x...1)
So you said that you needed more attempts (hundreds of thousands) to solve it, than, according to you, actual states exist. Isn't this a contradiction?
But that's from my point of view really not what CA asked.
3) or did you try to answer something completely else I missed?
All in all: I'm a bit confused. The question we want to answer seems to change from post to post. I'll quit this discussion for now and let CA pick whatever solution he wanted.
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Edit: I wrote up a reply to the 2x2 square, but deleted it. As long as the question is not clear, it's pretty pointless to discuss what was counted in which way. In short: I couldn't follow or reproduce the numbers. Of course it's possible to put the numbers in NOOCs text together that you get 8 or 10, but neither way seemed logical to me.
Oh well, so be it. It's just an online discussion... Have fun and enjoy life!