From 5e87743663d9cd54323593d0ffc7f7e31adb1e72 Mon Sep 17 00:00:00 2001 From: Sebastiano Tronto Date: Sat, 24 May 2025 16:37:15 +0200 Subject: Update figure it out guide with twizzle applets --- src/speedcubing/figure-it-out/comm1.png | Bin 10415 -> 0 bytes src/speedcubing/figure-it-out/comm1.svg | 39 ------------ src/speedcubing/figure-it-out/comm2.png | Bin 10603 -> 0 bytes src/speedcubing/figure-it-out/comm2.svg | 39 ------------ src/speedcubing/figure-it-out/edgecomm.png | Bin 10411 -> 0 bytes src/speedcubing/figure-it-out/edgecomm.svg | 39 ------------ src/speedcubing/figure-it-out/figure-it-out.md | 82 +++++++++++++++++++------ src/speedcubing/figure-it-out/setup.png | Bin 10278 -> 0 bytes src/speedcubing/figure-it-out/setup.svg | 39 ------------ src/speedcubing/figure-it-out/twist.png | Bin 10145 -> 0 bytes src/speedcubing/figure-it-out/twist.svg | 39 ------------ 11 files changed, 63 insertions(+), 214 deletions(-) delete mode 100644 src/speedcubing/figure-it-out/comm1.png delete mode 100644 src/speedcubing/figure-it-out/comm1.svg delete mode 100644 src/speedcubing/figure-it-out/comm2.png delete mode 100644 src/speedcubing/figure-it-out/comm2.svg delete mode 100644 src/speedcubing/figure-it-out/edgecomm.png delete mode 100644 src/speedcubing/figure-it-out/edgecomm.svg delete mode 100644 src/speedcubing/figure-it-out/setup.png delete mode 100644 src/speedcubing/figure-it-out/setup.svg delete mode 100644 src/speedcubing/figure-it-out/twist.png delete mode 100644 src/speedcubing/figure-it-out/twist.svg diff --git a/src/speedcubing/figure-it-out/comm1.png b/src/speedcubing/figure-it-out/comm1.png deleted file mode 100644 index cbc6112..0000000 Binary files a/src/speedcubing/figure-it-out/comm1.png and /dev/null differ diff --git a/src/speedcubing/figure-it-out/comm1.svg b/src/speedcubing/figure-it-out/comm1.svg deleted file mode 100644 index 6c41aad..0000000 --- a/src/speedcubing/figure-it-out/comm1.svg +++ /dev/null @@ -1,39 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - \ No newline at end of file diff --git a/src/speedcubing/figure-it-out/comm2.png b/src/speedcubing/figure-it-out/comm2.png deleted file mode 100644 index 69d3b63..0000000 Binary files a/src/speedcubing/figure-it-out/comm2.png and /dev/null differ diff --git a/src/speedcubing/figure-it-out/comm2.svg b/src/speedcubing/figure-it-out/comm2.svg deleted file mode 100644 index e69065b..0000000 --- a/src/speedcubing/figure-it-out/comm2.svg +++ /dev/null @@ -1,39 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - \ No newline at end of file diff --git a/src/speedcubing/figure-it-out/edgecomm.png b/src/speedcubing/figure-it-out/edgecomm.png deleted file mode 100644 index 6b4d230..0000000 Binary files a/src/speedcubing/figure-it-out/edgecomm.png and /dev/null differ diff --git a/src/speedcubing/figure-it-out/edgecomm.svg b/src/speedcubing/figure-it-out/edgecomm.svg deleted file mode 100644 index 6cffd65..0000000 --- a/src/speedcubing/figure-it-out/edgecomm.svg +++ /dev/null @@ -1,39 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - \ No newline at end of file diff --git a/src/speedcubing/figure-it-out/figure-it-out.md b/src/speedcubing/figure-it-out/figure-it-out.md index 5405d19..1c38657 100644 --- a/src/speedcubing/figure-it-out/figure-it-out.md +++ b/src/speedcubing/figure-it-out/figure-it-out.md @@ -1,3 +1,5 @@ + + # Rubik's cube: how to figure it out So you decided to try and solve a @@ -124,6 +126,14 @@ If you want some more hints, Ryan Heise's website contains some nice examples about building blocks in his [fundamental techniques page](https://www.ryanheise.com/cube/fundamental_techniques.html). +*Note: I have updated this page to use [twizzle](https://alpha.twizzle.net) +applets instead of simple pictures. These applets can be played to show the +solution. To experiment around with this solution, click on +the TW at the bottom right to open them in +[twizzle](https://alpha.twizzle.net/). In this way you can also +check which moves correspond to the written notation, if you +are not familiar with it.* + ## Commutators *In the rest of this page I am going to use the standard @@ -161,7 +171,13 @@ If you have not done it already, you should have a look at my page on Suppose that you manage, via blockbuilding, to reach the following state: -![A commutator](comm1.png) +
+ +
First of all, this would be an amazing achievement! The whole cube is solved except for three corners. The bottom-left corner (only one red @@ -220,21 +236,28 @@ the insertion sequence; then we have D', the inverse of the second move; and finally R, the inverse of the first move of the insertion sequence. * **U'**: the inverse of the interchange move. -To help understanding all of this, you can visualize this commutator -[alg.cubing.net](https://alg.cubing.net/?setup=%5BU,_R-DR%5D&alg=R-_D_R_%2F%2FInsertion%0AU_%2F%2FInterchange%0AR-_D-_R_%2F%2FInverse_insertion%0AU-_%2F%2FInverse_interchange). - **Note:** looking at the position of the pieces is not enough to determine a correct commutator to permute them. Their **orientation** is also important. For example, consider the following case: -![Another commutator](comm2.png) +
+ + +
The three corners are permuted in exactly the same way, so everything we said above could be repeated word by word, move by move. However, if you apply the commutator we constructed to this case, you'll get -something like this: +something like this (you can also see this by playing the applet above): -![Two twisted corners](twist.png) +
+ + +
What's wrong here? Well, obviously the cube is not solved. All the pieces are in their correct position, but two corners are twisted in place! @@ -246,7 +269,13 @@ but sometimes it is important to keep track of both. Let's highlight the difference between the two 3-cycles. In the first one: -![A commutator](comm1.png) +
+ +
1. The red-green-white corner must go to the place of the white-red-blue one, *with the white sticker of the first going to the place of the white sticker @@ -260,7 +289,14 @@ white sticker of the latter*. While in the second case: -![Another commutator](comm2.png) +
+ + +
1. The red-green-white corner must go to the place of the white-red-blue one, *with the white sticker of the first going to the place of the* **blue** *sticker @@ -281,16 +317,19 @@ white sticker of the red-green-white corner to the position of the red sticker of the white-red-blue one, while it should move it to the position of the blue sticker! -I won't repeat the whole construction for the second commutator, -but you can visualize a solution -[here](https://alg.cubing.net/?setup=%5BR-,_UL-U-%5D&alg=U_L-_U-_%2F%2FInsertion%0AR-_%2F%2FInterchange%0AU_L_U-_%2F%2FInverse_insertion%0AR_%2F%2FInverse_interchange). - ### Edge commutators So far I have only talked about *corner* commutators, but what if you are also left with some unsolved edges? For example, consider this case: -![A edge 3-cycle](edgecomm.png) +
+ + +
The picture shows a 3-cycle of edges. You might think that the same reasoning can be applied and that you can use commutators to solve @@ -301,7 +340,7 @@ Let's see how to solve the case above. As interchange move, you can use the **inner-layer move** E' (check out the [notation page](../notation) if you are unfamiliar with these). The insertion sequence to be used with it is L' U2 L. Putting everything together, you get -[E' L' U2 L E L' U2 L](https://alg.cubing.net/?setup=%5BL-U2L,E-%5D&alg=E-_%2F%2FInterchange%0AL-_U2_L_%2F%2FInsertion%0AE_%2F%2FInverse_interchange%0AL-_U2_L_%2F%2FInverse_insertion). +E' L' U2 L E L' U2 L. ### Commutators with set-up moves @@ -323,7 +362,15 @@ you need to use **set-up moves**, also known as Consider the following case: -![A 3-cycle of corners requiring a set-up move](setup.png) +
+ +
No matter how much you try, you are not going to find valid interchange and insertion moves as above. The fundamental problem is that you would @@ -353,9 +400,6 @@ putting it all together you get: **Note:** in this case the insertion coincides with its inverse. This can happen and there is nothing particular about it. -As usual, you can visualize the final result on -[alg.cubing.net](https://alg.cubing.net/?setup=L2B2R-F-RB2R-FRL2&alg=L_%2F%2FSet%26%2345%3Bup%0AU-_%2F%2FInterchange%0AR_D2_R-_%2F%2FInsertion%0AU_%2F%2FInverse_interchange%0AR_D2_R-_%2F%2FInverse_insertion%0AL-_%2F%2FInverse_set%26%2345%3Bup) - ## Conclusion With what you have learned so far, you can now try and solve the Rubik's diff --git a/src/speedcubing/figure-it-out/setup.png b/src/speedcubing/figure-it-out/setup.png deleted file mode 100644 index ac2bf6c..0000000 Binary files a/src/speedcubing/figure-it-out/setup.png and /dev/null differ diff --git a/src/speedcubing/figure-it-out/setup.svg b/src/speedcubing/figure-it-out/setup.svg deleted file mode 100644 index fa2360a..0000000 --- a/src/speedcubing/figure-it-out/setup.svg +++ /dev/null @@ -1,39 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - \ No newline at end of file diff --git a/src/speedcubing/figure-it-out/twist.png b/src/speedcubing/figure-it-out/twist.png deleted file mode 100644 index a1fb42a..0000000 Binary files a/src/speedcubing/figure-it-out/twist.png and /dev/null differ diff --git a/src/speedcubing/figure-it-out/twist.svg b/src/speedcubing/figure-it-out/twist.svg deleted file mode 100644 index 79e0a02..0000000 --- a/src/speedcubing/figure-it-out/twist.svg +++ /dev/null @@ -1,39 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - \ No newline at end of file -- cgit v1.3