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the 3 color 3x3x3 that has yellow opposite yellow, red opposite red, blue opposite blue can be solved using a different set of algorithms. I did not find a thread for this so I made one. there are 4 of each edge. there are 3 unique edge color combinations. there are 4 of each corner piece. there are 2 unique color patterns on the corners. the corners are mirrors of each other. the puzzle is solved in many alternate positions so long as each face contains 9 stickers of the same color. there are two of each center so be careful when you calculate the number of possible states of the cube.

so far I have only one algorithm. I noticed that I can use Gc Ga or Rb perm to finish the cube if the case is Gc Ga or Rb. it does not matter which one you use so you can just use the shortest one every time. from this we can also make a hypothesis that average number of moves to PLL will be reduced compared to 6 color 3x3x3. we can make another hypothesis that the number of PLL cases will be reduced from 19 to some smaller number. we already eliminated 4 cases if we drop all 4 G perms. H perm is a PLL skip also so we can drop that.

I want to know if there are shorter PLL's that swap pieces from the bottom layer with pieces from the top layer.

J PLL B' R' F R2 B' R F' R' 8 moves compared to R' U L' U2 R U' R' U2 R L U' 11 moves

T PLL R B2' R' U2 R2 U2 R B2' R' 9 moves compared to R U R' U' R' F R2 U' R' U' R U R' F' 14 moves

A PLL R' U R' D2 R U' R' 7 moves compared to R' U R' D2 R U' R' D2 R2 9 moves. this makes the T PLL obsolete.

Z PLL M2 U M2 U M2 5 moves replaces M2 U M2 U M' U2 M2 U2 M' U2 10 moves

so far I have only one algorithm. I noticed that I can use Gc Ga or Rb perm to finish the cube if the case is Gc Ga or Rb. it does not matter which one you use so you can just use the shortest one every time. from this we can also make a hypothesis that average number of moves to PLL will be reduced compared to 6 color 3x3x3. we can make another hypothesis that the number of PLL cases will be reduced from 19 to some smaller number. we already eliminated 4 cases if we drop all 4 G perms. H perm is a PLL skip also so we can drop that.

I want to know if there are shorter PLL's that swap pieces from the bottom layer with pieces from the top layer.

J PLL B' R' F R2 B' R F' R' 8 moves compared to R' U L' U2 R U' R' U2 R L U' 11 moves

T PLL R B2' R' U2 R2 U2 R B2' R' 9 moves compared to R U R' U' R' F R2 U' R' U' R U R' F' 14 moves

A PLL R' U R' D2 R U' R' 7 moves compared to R' U R' D2 R U' R' D2 R2 9 moves. this makes the T PLL obsolete.

Z PLL M2 U M2 U M2 5 moves replaces M2 U M2 U M' U2 M2 U2 M' U2 10 moves

Last edited: Jun 8, 2015