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Not slinging related but I need help ! lol (Read 248 times)
NooneOfConsequence
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Re: Not slinging related but I need help ! lol
Reply #15 - Dec 10th, 2019 at 9:35am
 
@Teg,
I cannot agree with your 4-number example. The grid is a construct intended to help quantify the problem, but the mental construct is not more important than the reality it represents. The reality is this: the pieces either fit, or they don’t.  In a 4-tile puzzle, the first piece can go anywhere, because the grid is relative, not absolute. 

If you know where the edge is, the second piece has three possible locations. Otherwise 5.  The third has two or four options depending on whether the second piece was the opposite corner of the first. The fourth only goes in one place. Maximum number of tests is 8.  Maximum number of moves is 10. If you pick opposing corners first, then max moves is 8.  If you can’t assume that the puzzle is in a 2x2 matrix, then the answer is obviously different too because you have to consider the 1x4 and “L” configurations too.

If you can’t know if the pieces fit, then all possibilities are equally correct and equally incorrect... In that case, your theoretical jigsaw puzzle is mathematically complete but useless as entertainment.
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“My final hour is at hand. We face an enemy more numerous and cunning than the world has yet seen. Remember your training, and do not fear the hordes of Judas. I, without sin, shall cast the first stone. That will be your sign to attack! But you shall not fight this unholy enemy with stones. No! RAZOR GLANDES!  Aim for the eyes! May the Lord have mercy, for we shall show none!“  -Jesus the Noodler
 
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NooneOfConsequence
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Re: Not slinging related but I need help ! lol
Reply #16 - Dec 10th, 2019 at 10:12am
 
Ok, here’s a mathier way to explain it:

A matrix is the wrong model. People use a “graph-based” approach. It’s not a grid. It’s a vector map.
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“My final hour is at hand. We face an enemy more numerous and cunning than the world has yet seen. Remember your training, and do not fear the hordes of Judas. I, without sin, shall cast the first stone. That will be your sign to attack! But you shall not fight this unholy enemy with stones. No! RAZOR GLANDES!  Aim for the eyes! May the Lord have mercy, for we shall show none!“  -Jesus the Noodler
 
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Teg
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Re: Not slinging related but I need help ! lol
Reply #17 - Dec 10th, 2019 at 3:09pm
 
@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 6th, 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 6th, 2019 at 5:52pm:
The maximum number of states for an 8x8 puzzle is  16640.

but you also say:
NooneOfConsequence wrote on Dec 6th, 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.

----------
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!


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NooneOfConsequence
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Re: Not slinging related but I need help ! lol
Reply #18 - Dec 10th, 2019 at 8:09pm
 
In a graph-based model, you can take multiple paths to reach the same final state. I probably didn’t explain it very well though.
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“My final hour is at hand. We face an enemy more numerous and cunning than the world has yet seen. Remember your training, and do not fear the hordes of Judas. I, without sin, shall cast the first stone. That will be your sign to attack! But you shall not fight this unholy enemy with stones. No! RAZOR GLANDES!  Aim for the eyes! May the Lord have mercy, for we shall show none!“  -Jesus the Noodler
 
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Curious Aardvark
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Re: Not slinging related but I need help ! lol
Reply #19 - Dec 17th, 2019 at 12:16pm
 
see now all I was thinking about were factorals and which bits to divide by and/or subtract.

But hey, it's kept you guys occupied for a while Smiley
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Do All things with Honour and Generosity: Regret Nothing, Envy None, Apologise Seldom and Bow your head to No One  - works for me Smiley
 
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Eudave
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Re: Not slinging related but I need help ! lol
Reply #20 - Jan 29th, 2020 at 2:28pm
 
joe meadmaker
if my calculator is correct and you simply want them all to be placed in a line in all possible changes  then the answer is 1.26886932185888416410343338933516e+89
The earth will be a fireball in less than that number of seconds
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joe_meadmaker
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Re: Not slinging related but I need help ! lol
Reply #21 - Jan 31st, 2020 at 2:57pm
 
Eudave wrote on Jan 29th, 2020 at 2:28pm:
joe meadmaker
if my calculator is correct and you simply want them all to be placed in a line in all possible changes  then the answer is 1.26886932185888416410343338933516e+89
The earth will be a fireball in less than that number of seconds

There's definitely a lot.  Of all these calculations, I couldn't tell you which one is accurate.  But I think we can agree on one thing.  CA, if you decide to make a puzzle, you need to make it easier. Cheesy
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