KottenCube
Member
Now please don't go asking for bigger cube god numbers. It took day with Google computers for a 3x3, imagine how long it would take them with a 4x4.
There's 7.4x10^45 and a 3x3 has 4.3x10^18 so if it takes one day to do 43 quintillion(4.3x10^18) it would take approx years (no calulator likes you putting in the 7.4x10^45 or at least true iOS one)
but when you add in the increased speed and strength and power of technology and computers, I estimate that Google could crack it in about 2 years. I wonder how fast it could be calculated if you used all the supercomputers and processing power that the US government uses... Not that that would happen, of course, but I bet that could do it in 6 months to a year.
I'd like to see how you calculated those times.
I think it's absolutely fair to say that this won't be computed in the lifetime of anyone on this forum now.
You never know stillI think it's absolutely fair to say that this won't be computed in the lifetime of anyone on this forum now.
1^3 - 1^2 + 1^2 - 1^0 = 0
2^3 + 2^2 - 2^2 + 2^0 = 11
3^3 - 3^2 + 3^1 - 3^0 = 20
4^3 + 4^2 - 4^2 + 4^0 = 77
5^3 - 5^2 + 5^5 - 5^0 = 104
i'm going to make a wild guess that it's 77 single layer turns.
i found the pattern below which holds for n=1 to 3.
1^3 - 1^2 + 1^2 - 1^0 = 0
2^3 + 2^2 - 2^2 + 2^0 = 11
3^3 - 3^2 + 3^1 - 3^0 = 20
4^3 + 4^2 - 4^2 + 4^0 = 77
5^3 - 5^2 + 5^5 - 5^0 = 104
etc.
i doubt it's correct but i thought i would share.
i saw the current upper bound on n=4 is 77 here: http://cubezzz.dyndns.org/drupal/?q=node/view/93
so we just need to get it lower than 77 to throw away this pattern.
Obviously you made a few typos (I fixed them in the quote above), but writing this pattern as a formula, it gives a value of 8381 slice half turns for the 20x20x20. I attempted to make a formula myself for this while back, and it seemed to give values larger than what God's number probably is for very large cubes. Based on my formula, GN for the 20x20x20 cannot be more than 867 slice half turns, and Mr. Rokicki claims that it must be at least 682. Even if GN for n = 20 is 1500 slice half turns, 8381 is a lot more (which also supports qqwref's comment). So 77 is most likely too high (based on my formula, it's going to be at most 63...it's most likely in the mid 40s).i'm going to make a wild guess that it's 77 single layer turns.
i found the pattern below which holds for n=1 to 3.
1^3 - 1^2 + 1^1 - 1^0 = 0
2^3 + 2^2 - 2^1 + 2^0 = 11
3^3 - 3^2 + 3^1 - 3^0 = 20
4^3 + 4^2 - 4^1 + 4^0 = 77
5^3 - 5^2 + 5^1 - 5^0 = 104
etc.
so we just need to get it lower than 77 to throw away this pattern.
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