I doubt that there is any pattern for God's numbers. Just because the 2x2 and 3x3 and 4x4 are very different compared to each other (3x3 has no center pieces, 2x2 has no edges nor centerpieces). I don't think they fit in a scheme in that way.
For the Fibonacci numbers at least, there is an easy and very accurate approximation expression:
F(n)=(1/sqrt(5))*G^n where G = Golden ratio = (1 + sqrt(5))/2
Example #1: n=5, F(5)=4.95967...... , exact value of F(5)=5
Example #2: n=2, F(2)=1.17082......, exact value of F(2)=1
Well, an n x n x n cube can be optimally solved with Θ(n2 / log(n)) moves. [by Wikipedia]
But I don't know how to do this calculation
31 is my estimate now since if you only turn two layers it reduced to a 2x2 and gods number for a 2x2 is 11 and if you only turn the outer layers it reduced to a 3x3 which gods number is 20 abd 20+11=31
opitmal reduction isn't the shortest 4x4 solution. Still finding this out will be hard what about the 13ish quintillion solutions that look like a 3x3 but have parity can't that be solved in 11 movesYou need to pair up edges and put them in the right spot relative to your centers as well.
Well, no. Here is a counterexample: apply the following 6-move scramble:opitmal reduction is the shortest 4x4 solution.
Don't trust Wikipedia to get everything correct. As far as I know, a method of solving an nxnxn cube which was of Θ(n^2 / log(n)) was found. That provides an upper bound of how fast God's number grows, it doesn't say how fast it grows or what the formula for God's number actually is (assuming such a formula can ever be found).
Well, no. Here is a counterexample: apply the following 6-move scramble:
Lw' U R' U' Lw R2
Now perform optimal reduction:
x' Rw'' D R' D' Rw (5 moves)
If optimal reduction yielded the shortest solution, you should be able to finish the solve in 1 move or less by now. This is obviously not the case.
Please don't illegitimately badmouth Wikipedia, especially when it's you who doesn't know the difference between O and Θ.
31 is my estimate now since if you only turn two layers it reduced to a 2x2 and gods number for a 2x2 is 11 and if you only turn the outer layers it reduced to a 3x3 which gods number is 20 abd 20+11=31
*cringe*
Really, "minimum" number?! :fp
Thread starter | Similar threads | Forum | Replies | Date |
---|---|---|---|---|
When do you think will there be a sub god's number fmc mean OFFICALLY | General Speedcubing Discussion | 4 | ||
M | Dodecahedron (and other) God's Numbers | Puzzle Theory | 2 | |
K | God's Number for CFOP and Roux | Puzzle Theory | 26 | |
4x4x4 God's Number Position Hunt | Puzzle Theory | 50 | ||
S | God's Number for 4x4 Found! | General Speedcubing Discussion | 93 |