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We all know that God's number for a 3x3x3 Rubik's cube is 20 moves. But I have been wondering lately what is God's number for a 4x4x4 Rubik's cube? :confused:

It's been proven to be at least 33 (according to multiple sites), but as far as I know we don't even have an upper bound. What I want to know is how they got the lower bound

It's been proven to be at least 33 (according to multiple sites), but as far as I know we don't even have an upper bound. What I want to know is how they got the lower bound

prove that you can't select all four aces in the deck of cards with only three selections.
now imagine that after you have selected one card from deck you return it and remove few non-aces cards from the deck depnding on last selected card... all the way to be left with only 4 cards, which are, of course 4 aces.
similar principle.

waiting to super-uber-computers to calculate all the states of 4x4 and fewest move solve for each one.
one can't simply calculate the 4God's number, but dozens can.

That was 35 years of CPU time. That's a rounding error to projects like SETI at home.

Nonetheless a 4x4 would require an astronomical amont more. Probably more than all the distributed computing projects put together.
Plus interested qualified people doing the coding.

Will the diameter of the 4x4x4 be known in my lifetime? I suspect it will be, despite the fact that just solving a single random 4x4x4 position optimally probably requires more CPU time using current techniques than were used to determine the diameter of the 3x3x3

Indeed... and there are about 10^26 million times as many 4x4 positions as there are 3x3 positions (that's a hundred million million million million). So even if it was as easy to solve a 4x4 scramble optimally as it is to solve a 3x3 scramble optimally, we'd still need a hundred million million million million times as long to get God's Algorithm as we took to do it for the 3x3...

Considering we're only a few orders of magnitude from the atomic computing limit, I feel like I can predict that this computation cannot be done using our current knowledge of optimal-solving techniques.

Indeed... and there are about 10^26 million times as many 4x4 positions as there are 3x3 positions (that's a hundred million million million million). So even if it was as easy to solve a 4x4 scramble optimally as it is to solve a 3x3 scramble optimally, we'd still need a hundred million million million million times as long to get God's Algorithm as we took to do it for the 3x3...

Considering we're only a few orders of magnitude from the atomic computing limit, I feel like I can predict that this computation cannot be done using our current knowledge of optimal-solving techniques.

prove that you can't select all four aces in the deck of cards with only three selections.
now imagine that after you have selected one card from deck you return it and remove few non-aces cards from the deck depnding on last selected card... all the way to be left with only 4 cards, which are, of course 4 aces.
similar principle.

waiting to super-uber-computers to calculate all the states of 4x4 and fewest move solve for each one.
one can't simply calculate the 4God's number, but dozens can.