irontwig
Member
On to 4x4!
Edit: This isn't serious. Not at this point in time, at least.
What about 2x2?
http://www.jaapsch.net/puzzles/cube2.htm
On to 4x4!
Edit: This isn't serious. Not at this point in time, at least.
What about 2x2?
On to 4x4!
Edit: This isn't serious. Not at this point in time, at least.
What about 2x2?
On to 4x4!
Edit: This isn't serious. Not at this point in time, at least.
What about 2x2?
I'm wondering if it's a coincidence how there is exactly 20 pieces (12 edges and 8 corners.) This is excluding the core but that doesn't change position.
I wonder if God's Number for 2x2 would be 8 moves.
Anyway, this is amazing.
"Distance-20 positions are both rare and plentiful; they are rarer than one in a billion positions, yet there are probably more than one hundred million such positions. We do not yet know exactly how many there are."Exactly how many positions are of maximum distance from solved? And are all these symmetrical positions??
Per
Now that they know which solutions need 20 moves, they could take a look specifically at those, and try to reduce the numbers... right?
Now that they know which solutions need 20 moves, they could take a look specifically at those, and try to reduce the numbers... right?
"Distance-20 positions are both rare and plentiful; they are rarer than one in a billion positions, yet there are probably more than one hundred million such positions. We do not yet know exactly how many there are."Exactly how many positions are of maximum distance from solved? And are all these symmetrical positions??
Per
If there was an exhaustive search that number should be known. Or could have easily been known if implemented Oh well, my main concern was the second question...
Because the 2x2x2 has so little permutations, it can easily be brute forced. Here's a table. God's number is 11 for a 2x2x2.
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Although I'm curious how they came to their conclusion that "FU-F2D-BUR-F-LD-R-U-LUB-D2R-FU2D2" was the hardest solve for the computers.
For a coset of the subgroup H=<U,D,R2,L2,F2,B2> which has about 20 billion elements we generated in principle (because we need only one bit per element) the optimal solutions for all elements of this coset which have <=15 moves and eventually a fraction of all elements which have 16 moves. Appending now 5 moves (15) or 4 moves (16) only from subgroup H nonoptimal-solutions for almost all other elements of the coset are generated. This reminds in some way on the two-phase algorithm and there is indeed a close connection to the method.
R' U2 B L' F U' B D F U D' L D2 F' R B' D F' U' B' U D'.
It's on the page.
Before you guys start on the 4x4x4 and 5x5x5 I'll guess... 30 and 42.
Before you guys start on the 4x4x4 and 5x5x5 I'll guess... 30 and 42.
That sounds way low, as the 4x4x4 has more than twice the number of pieces than the 3x3x3. If I would guess the 4x4x4 would be closer to 40 moves. Does anybody know upper and lower bounds of the 4x4x4?