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-rw-r--r--src/speedcubing/no-cube/no-cube.md68
-rw-r--r--src/speedcubing/speedcubing.md2
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diff --git a/src/speedcubing/no-cube/no-cube.md b/src/speedcubing/no-cube/no-cube.md
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1# Solving a cube... without a cube
2
3*In this page you can find the full text of a message I posted on the
4[speedsolving forum](https://www.speedsolving.com/forum/threads/the-3x3x3-example-solve-thread.14345/page-273#post-1173067)
5in 2016. It is the explanation of how I managed to write down a solution
6for a 3x3x3 Rubik's Cube scramble using just pen an paper, without
7a cube.*
8
9**Scramble**: B R2 B2 R' U2 R2 D2 L B2 F2 R2 D R' U' R U' L2 R D2 B'
10
11For this scramble, I have tried something I have had in my mind for
12quite a long time. I have found this solution without using any cube
13(physical nor simulator). As I would do in a blind solve, I solved edges
14and corners separately with commutators. First, I tracked every edge
15to see the permutation cycle (and check if there were any flipped). This
16was easier than I had thought. I have found this.
17
18(UR BU DR FL LB FR BD DF UF UL)(DL RB)
19
20Now I use commutators to "solve" these cycles. Actually I "copy" these
21cycle, so I am matching the scramble instead of solving it. No big deal,
22I just have to invert the final solution to get one for this scramble.
23The easiest way would be to just do a blind solve, but I struggled
24I little bit to save moves, in order to see if I could get under the
2580HTM limit for a legal FMC solve. I could break the first big cycle
26into 3-cycles in any order, and I choose this one. There are probably
27better ways to solve edges, but I didn't want to think to much about it.
28
29(A) (UF UL UR) = [F2 U: M', U2] = F2 U R' L F2 R L' U F2
30(B) (UF BU DR) = [M', B' R B] = R' L U' R' U R L' B' R B
31\(C\) (UF FL LB) = [L' U L, E] = L' U L U D' B' U' B U' D
32(D) (UF FR BD) = [U2: M, U R U'] = U2 R L' B R B' R' L U R' U
33
34Then I solve the 2-2 cycle left.
35
36(E) (UF DF)(DL RB) = [U B U': (L2 F2)3] = U B U' L2 F2 L2 F2 L2 F2 U B' U'
37
38Same thing for corners. One was twisted, so I use a different notation
39for the permutation.
40
41UBL->BLU
42UFL->LFD->DBR->UFR->RFD->LBD->URB->FUL
43
44(1) (UBL UFL LFD) = [U', L D L] = U' L D L' U L D' L'
45(2) (URB FUL UBL) = [F R' F', L] = F R' F' L F R F' L'
46(3) (UFR RFD LBD) = [R U R', D2] = R U R' D2 R U' R' D2
47(4) (DBR UFR URB) = [D: B2, D F2 D'] = D B2 D F2 D' B2 D F2 D2
48
49Now I can use this commutators in any order, as long as the relative
50order of the pieces of the same kind remains the same (i.e. I cannot use
51(2) before (1), but I can do either (A) (B) (1), (A) (1) (B), (1) (A)
52(B)). To cancel more moves, I used this order:
53
54(1) (A) (2) (B) \(C\) (D) (E) (3) (4)
55
56At this point I checked the solution on my cube and it was extremely
57satisfactory to see everything going as I expected :) Inverting and
58cancelling gives the following solution:
59
60D2 F2 D' B2 D F2 D' B2 D R U R' D2 R U' R' U B U' F2
61L2 F2 L2 F2 L2 U B' U2 R U' L' R B R' B' L R' U' D' B'
62U B D U' L' U' L B' R' B L R' U' R U R F R' F' L'
63F R F U' L R' F2 L' R U' F2 L D L' U' L D' L' U
64
65alg.cubing.net
66
6779 HTM, just under the limit :) There are many ways to improve this
68"method", but I just wanted a success, and I am satisfied with the result.
diff --git a/src/speedcubing/speedcubing.md b/src/speedcubing/speedcubing.md
index a16a0e1..d1e2057 100644
--- a/src/speedcubing/speedcubing.md
+++ b/src/speedcubing/speedcubing.md
@@ -65,4 +65,4 @@ They are outdated and not very good, I may upload a better version at some point
65 65
66* [My WCA profile](https://www.worldcubeassociation.org/persons/2011TRON02) 66* [My WCA profile](https://www.worldcubeassociation.org/persons/2011TRON02)
67* [My YouTube channel](https://www.youtube.com/c/SebastianoTronto) 67* [My YouTube channel](https://www.youtube.com/c/SebastianoTronto)
68* [Solving a cube... without a cube](https://www.speedsolving.com/forum/threads/the-3x3x3-example-solve-thread.14345/page-273#post-1173067) 68* [Solving a cube... without a cube](no-cube)

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