Discomantis
Member
What are the exact odds of getting one or more four move 2x2 scrambles in your first 2x2 round? (
According to Wikipedia, there are 1847 out of 3674160 positions that can be solved optimally in 4 moves(assuming HTM). There are also 385 scrambles that are illegal according to wca regs, meaning 3671928 out of 3673775 legal scrambles are NOT 4 movers. That gives a \( \left(\frac{3671928}{3673775}\right)^5\approx99.7\% \) chance of no 4 movers in 5 solves, so the answer is about 100-99.7=0.3%.What are the exact odds of getting one or more four move 2x2 scrambles in your first 2x2 round? (
I believe it would be (4!*2^4)Which equals 1/768. I could be extremely off, but I’ll explain my reasoning.What are the odds of a CN standard CFOP cross being solved, where being offset by a D/D'/D2 counts as solved
Essentially a pre-built cross, but not aligned.
I tried to work this out myself and got 1/7925.98587297, ofc rounding to 1/7926 for simplicity's sake.
However I am very bad at maths and have most likely gotten something wrong.
4 edges in the right spot is not 1/4!. There are 12 edges on a cube if I counted correctly, and you need them to be in the right order relative to each other so 4! doesn't work. This also only considers one color cross.I believe it would be (4!*2^4)Which equals 1/768. I could be extremely off, but I’ll explain my reasoning.
You have to have 4 edges in the right spot (4!). You need 4 edges oriented correctly (2^4). Then you multiply them and get 1/768.
// EP = 12!/4!F2l skip possibility
12! = 12 x 11 x 10 x [...] x 1I dont understand Hieroglyphics
wait until you find about generating functionsI dont understand Hieroglyphics
What are the odds of a CN standard CFOP cross being solved, where being offset by a D/D'/D2 counts as solved
Essentially a pre-built cross, but not aligned.
I tried to work this out myself and got 1/7925.98587297, ofc rounding to 1/7926 for simplicity's sake.
However I am very bad at maths and have most likely gotten something wrong.
That scramble is really good, easy 1 look F2L on orange. I'm a white-yellow solver and still managed to get 6.06 on a colour I never do and a cube I never useWhat's the odd of getting a scramble with two 2×2×1 block?
(Got this scramble few minutes ago:
R2 B2 L2 D' B2 D2 L2 F2 R2 F2 R2 U2 R' F L2 B' L D' R' D' R' )
100%possibility of me understanding any of the numbers on this thread?
ive gone through the thread on multiple occasions, it all flies right over my head100%
There is going to be at least one thing you understand in this thread
For a set of two corners and four edges the number of permutations is given by:What's the odd of getting a scramble with two 2×2×1 block?
(Got this scramble few minutes ago:
R2 B2 L2 D' B2 D2 L2 F2 R2 F2 R2 U2 R' F L2 B' L D' R' D' R' )
side note, crazy scramble. acn linkWhat's the odd of getting a scramble with two 2×2×1 block?
(Got this scramble few minutes ago:
R2 B2 L2 D' B2 D2 L2 F2 R2 F2 R2 U2 R' F L2 B' L D' R' D' R' )
For a set of two corners and four edges the number of permutations is given by:
(24 * 21) * (24 * 22 * 20 * 18) = 95,800,320
So for the example you give the odds are 1 in 95,800,320. With rotation and mirror symmetry there are 48 equivalent patterns of this type.
However there are a number of different ways of having two 2x2 blocks. For example one could have
F' R F' B U' B' L2 B L F U' B' U F' U B2 L'
or
F R U' R D' L' U R' U' F' L U' F R' F U' D R F'
I haven't counted up all the distinct ways one could have two solved 2x2 blocks but they would all have similar probabilities.
ADDENDUM
After playing around with a cube editor, I composed the following ten ways of having two 2x2 patches on two adjacent cube faces and had not exhausted all the possibilities. And then there are all the cases where the 2x2 patches are on opposite faces. I'd guess there are probably in excess of 20 types in total. Each type would then have 48 symmetry equivalent patterns. So, I'd estimate that the odds of getting two 2x2x1 blocks with a random scramble would be something like 1 in 100,000.
Type 1
U B U' D' F2 L' F D' R U L F' L' F' U D L
Type 2
U R' F D' L B U B D R F L' F' B' U B' D R' F R'
Type 3
L' F R' B R2 U' D F' U' F' R F' R' D' R B' R' L
Type 4
U R2 U B R' U' D' L F D2 B' L' B R L U' L2 B'
Type 5
R' U R2 D L D' F' B D' B' D F' B D' F D' F' B' R L
Type 6
R' U R F D R D' R B' R' D' F2 R B' R' F' D' L' D L
Type 7
L2 D F R L U' F' L' F2 D B' R B U D' F' U
Type 8
L U' D' F' L F D' R' L U' R' F R2 U B2 L F L
Type 9
U R2 U F D R' F B L' D' B2 D2 R' B' R F'
Type 10
F' U L' U R D' B D L' B R' U' B' U' F' B L' F' R'