Joel Banks
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- Apr 27, 2016
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We recently learned for sure that Gods number for the 3x3 is 20. What is (and how would we find) Gods number for a 4x4? There are ~ 7.4 quattordecillion combinations.
Gods number 4x4
- Thread starter Joel Banks
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shadowslice e
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Unless someone can find an elegant mathematical description of the cube which can be used to produce the width of a cube group for a cube of a certain size, the only way to do it is proof by exhaustion which was what was used for the 2x2 and 3x3 cubes. However, the amount of time required to this for a 4x4, while not beyond today's supercomputers is still definitely more than anyone with access to such machines would be willing to use especially as the "branches" for each tree will become about x^36 (i think; i didn't really think it through too hard) time more numerous for each depth for 4x4 using OBTM.
That said, we can establish lower bounds for God's number by proving that a position is optimally solvable in n moves. This was done on 3x3 where it was conjecture that the superflip and supertwist positions were very hard to solve and both ended up using 20 moves hence giving the lower bound at 20.
That said, we can establish lower bounds for God's number by proving that a position is optimally solvable in n moves. This was done on 3x3 where it was conjecture that the superflip and supertwist positions were very hard to solve and both ended up using 20 moves hence giving the lower bound at 20.
