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authorSebastiano Tronto <sebastiano@tronto.net>2025-05-24 16:37:15 +0200
committerSebastiano Tronto <sebastiano@tronto.net>2025-05-24 16:37:15 +0200
commit5e87743663d9cd54323593d0ffc7f7e31adb1e72 (patch)
tree2a1ea88e70be3a32b595cca12928630471a5d431 /src/speedcubing
parentd255058a4618d5f434eeabe4a1b8cc26e782a7d9 (diff)
downloadsebastiano.tronto.net-5e87743663d9cd54323593d0ffc7f7e31adb1e72.tar.gz
sebastiano.tronto.net-5e87743663d9cd54323593d0ffc7f7e31adb1e72.zip
Update figure it out guide with twizzle applets
Diffstat (limited to 'src/speedcubing')
-rw-r--r--src/speedcubing/figure-it-out/comm1.pngbin10415 -> 0 bytes
-rw-r--r--src/speedcubing/figure-it-out/comm1.svg39
-rw-r--r--src/speedcubing/figure-it-out/comm2.pngbin10603 -> 0 bytes
-rw-r--r--src/speedcubing/figure-it-out/comm2.svg39
-rw-r--r--src/speedcubing/figure-it-out/edgecomm.pngbin10411 -> 0 bytes
-rw-r--r--src/speedcubing/figure-it-out/edgecomm.svg39
-rw-r--r--src/speedcubing/figure-it-out/figure-it-out.md82
-rw-r--r--src/speedcubing/figure-it-out/setup.pngbin10278 -> 0 bytes
-rw-r--r--src/speedcubing/figure-it-out/setup.svg39
-rw-r--r--src/speedcubing/figure-it-out/twist.pngbin10145 -> 0 bytes
-rw-r--r--src/speedcubing/figure-it-out/twist.svg39
11 files changed, 63 insertions, 214 deletions
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
--- a/src/speedcubing/figure-it-out/comm1.png
+++ /dev/null
Binary files 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 @@
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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
--- a/src/speedcubing/figure-it-out/comm2.png
+++ /dev/null
Binary files 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 @@
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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
--- a/src/speedcubing/figure-it-out/edgecomm.png
+++ /dev/null
Binary files 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
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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 @@
1<script src="https://cdn.cubing.net/v0/js/cubing/twisty" type="module"></script>
2
1# Rubik's cube: how to figure it out 3# Rubik's cube: how to figure it out
2 4
3So you decided to try and solve a 5So you decided to try and solve a
@@ -124,6 +126,14 @@ If you want some more hints, Ryan Heise's website contains some nice
124examples about building blocks in his 126examples about building blocks in his
125[fundamental techniques page](https://www.ryanheise.com/cube/fundamental_techniques.html). 127[fundamental techniques page](https://www.ryanheise.com/cube/fundamental_techniques.html).
126 128
129*Note: I have updated this page to use [twizzle](https://alpha.twizzle.net)
130applets instead of simple pictures. These applets can be played to show the
131solution. To experiment around with this solution, click on
132the TW at the bottom right to open them in
133[twizzle](https://alpha.twizzle.net/). In this way you can also
134check which moves correspond to the written notation, if you
135are not familiar with it.*
136
127## Commutators 137## Commutators
128 138
129*In the rest of this page I am going to use the standard 139*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
161 171
162Suppose that you manage, via blockbuilding, to reach the following state: 172Suppose that you manage, via blockbuilding, to reach the following state:
163 173
164![A commutator](comm1.png) 174<center>
175<twisty-player experimental-setup-alg="[U, R' D R]"
176alg="R' D R // Insertion
177 U // Interchange
178 R' D' R // Inverse insertion
179 U' // Inverse interchange"></twisty-player>
180</center>
165 181
166First of all, this would be an amazing achievement! The whole cube is 182First of all, this would be an amazing achievement! The whole cube is
167solved except for three corners. The bottom-left corner (only one red 183solved 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;
220and finally R, the inverse of the first move of the insertion sequence. 236and finally R, the inverse of the first move of the insertion sequence.
221* **U'**: the inverse of the interchange move. 237* **U'**: the inverse of the interchange move.
222 238
223To help understanding all of this, you can visualize this commutator
224[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).
225
226**Note:** looking at the position of the pieces is not enough to 239**Note:** looking at the position of the pieces is not enough to
227determine a correct commutator to permute them. Their **orientation** 240determine a correct commutator to permute them. Their **orientation**
228is also important. For example, consider the following case: 241is also important. For example, consider the following case:
229 242
230![Another commutator](comm2.png) 243<center>
244<twisty-player experimental-setup-alg="[R', U L' U']"
245alg="R' D R // Insertion
246 U // Interchange
247 R' D' R // Inverse insertion
248 U' // Inverse interchange"></twisty-player>
249</twisty-player>
250</center>
231 251
232The three corners are permuted in exactly the same way, so everything 252The three corners are permuted in exactly the same way, so everything
233we said above could be repeated word by word, move by move. However, 253we said above could be repeated word by word, move by move. However,
234if you apply the commutator we constructed to this case, you'll get 254if you apply the commutator we constructed to this case, you'll get
235something like this: 255something like this (you can also see this by playing the applet above):
236 256
237![Two twisted corners](twist.png) 257<center>
258<twisty-player experimental-setup-alg="[U, R' D' R D R' D' R]">
259</twisty-player>
260</center>
238 261
239What's wrong here? Well, obviously the cube is not solved. All the pieces 262What's wrong here? Well, obviously the cube is not solved. All the pieces
240are in their correct position, but two corners are twisted in place! 263are 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.
246 269
247Let's highlight the difference between the two 3-cycles. In the first one: 270Let's highlight the difference between the two 3-cycles. In the first one:
248 271
249![A commutator](comm1.png) 272<center>
273<twisty-player experimental-setup-alg="[U, R' D R]"
274alg="R' D R // Insertion
275 U // Interchange
276 R' D' R // Inverse insertion
277 U' // Inverse interchange"></twisty-player>
278</center>
250 279
2511. The red-green-white corner must go to the place of the white-red-blue one, 2801. The red-green-white corner must go to the place of the white-red-blue one,
252*with the white sticker of the first going to the place of the white sticker 281*with the white sticker of the first going to the place of the white sticker
@@ -260,7 +289,14 @@ white sticker of the latter*.
260 289
261While in the second case: 290While in the second case:
262 291
263![Another commutator](comm2.png) 292<center>
293<twisty-player experimental-setup-alg="[R', U L' U']"
294alg="U L' U' // Insertion
295 R' // Interchange
296 U L U' // Inverse insertion
297 R // Inverse interchange"></twisty-player>
298</twisty-player>
299</center>
264 300
2651. The red-green-white corner must go to the place of the white-red-blue one, 3011. The red-green-white corner must go to the place of the white-red-blue one,
266*with the white sticker of the first going to the place of the* **blue** *sticker 302*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
281red sticker of the white-red-blue one, while it should move it 317red sticker of the white-red-blue one, while it should move it
282to the position of the blue sticker! 318to the position of the blue sticker!
283 319
284I won't repeat the whole construction for the second commutator,
285but you can visualize a solution
286[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).
287
288### Edge commutators 320### Edge commutators
289 321
290So far I have only talked about *corner* commutators, but what if you 322So far I have only talked about *corner* commutators, but what if you
291are also left with some unsolved edges? For example, consider this case: 323are also left with some unsolved edges? For example, consider this case:
292 324
293![A edge 3-cycle](edgecomm.png) 325<center>
326<twisty-player experimental-setup-alg="[L' U2 L, E']"
327alg="E' // Interchange
328 L' U2 L // Insertion
329 E // Inverse interchange
330 L' U2 L // Inverse insertion"></twisty-player>
331</twisty-player>
332</center>
294 333
295The picture shows a 3-cycle of edges. You might think that the same 334The picture shows a 3-cycle of edges. You might think that the same
296reasoning can be applied and that you can use commutators to solve 335reasoning 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
301the **inner-layer move** E' (check out the [notation page](../notation) 340the **inner-layer move** E' (check out the [notation page](../notation)
302if you are unfamiliar with these). The insertion sequence to be used 341if you are unfamiliar with these). The insertion sequence to be used
303with it is L' U2 L. Putting everything together, you get 342with it is L' U2 L. Putting everything together, you get
304[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). 343E' L' U2 L E L' U2 L.
305 344
306### Commutators with set-up moves 345### Commutators with set-up moves
307 346
@@ -323,7 +362,15 @@ you need to use **set-up moves**, also known as
323 362
324Consider the following case: 363Consider the following case:
325 364
326![A 3-cycle of corners requiring a set-up move](setup.png) 365<center>
366<twisty-player experimental-setup-alg="[L: [R D2 R', U']]"
367alg="L // Set-up
368 U' // Interchange
369 R D2 R' // Insertion
370 U // Inverse interchange
371 R D2 R' // Inverse insertion
372 L' // Inverse set-up"></twisty-player>
373</center>
327 374
328No matter how much you try, you are not going to find valid interchange 375No matter how much you try, you are not going to find valid interchange
329and insertion moves as above. The fundamental problem is that you would 376and insertion moves as above. The fundamental problem is that you would
@@ -353,9 +400,6 @@ putting it all together you get:
353**Note:** in this case the insertion coincides with its inverse. This 400**Note:** in this case the insertion coincides with its inverse. This
354can happen and there is nothing particular about it. 401can happen and there is nothing particular about it.
355 402
356As usual, you can visualize the final result on
357[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)
358
359## Conclusion 403## Conclusion
360 404
361With what you have learned so far, you can now try and solve the Rubik's 405With 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
--- a/src/speedcubing/figure-it-out/setup.png
+++ /dev/null
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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
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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
--- a/src/speedcubing/figure-it-out/twist.png
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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
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