Changes between Initial Version and Version 1 of RubikCubeSolving Tweet

Timestamp:

08/13/2008 09:18:27 PM (16 years ago)

Author:

kali

Comment:

first draft on cube constraints

RubikCubeSolving

@@ +1 @@
+= Overview =
+
+Once the color reduction issue is fixed, we have several other interesting problems still at hand.
+
+ * computing configurations of cubes : from images to finished cubes.
+ * implementing these configuration in real life on six hundred cubes : from defined computer known cubes configurations to physical world.
+
+= Computing cubes =
+
+== Constraints on Rubik's cubes ==
+
+The pixels displayed with facelets on each side of the cube can not adopt any combination.
+
+Some constraints are imposed by the cubies themselves:
+ * the two center facelets have two colours from opposites sides of the cube
+ * no more than four corner facelets (out of height, four on each face) or four edge facelets can show the same colour
+ * there are more constraints, but they are more difficult to express. Let's assume white is opposite yellow ; if we consider only corner facelets, it is not valid to display four white pixels and three blue on the same cube, as there are four corner cubies with a blue facelet, but two of them are required to show white pixels... We may want to be more specific here, and get an exact expression of which combination are permited.
+
+And there are also "parity" constraints imposed by the cube permutations : if one break a cube apart, using a screwdriver, and put it back together randomly, eleven time out of twelve, the cube will reach a state that can not be "solved". More specifically, if a cube is in a "valid" configuration: 
+ 1. there is always an even number of edges that are flipped,
+ 2. the sum of elementary rotation on corner cubies is always a multiple of three,
+ 3. the total number of permutation of cubies (including both corners and edges) is even.
+
+As we will have four hidden edge cubies, we can accomodate constraints 1 and 3 can be arranged with no difficulty. Obviously the second one remains an issue.
+
+= Implementing configuration =
+
+= Links =