3 ms·
The whole point is that in a way, there is that constant function that you say doesn't exist. Or more specifically, there is a fixed sequence of moves that wil
by BoiledCabbage 2y ago
The whole point is that in a way, there is that constant function that you say doesn't exist.
Or more specifically, there is a fixed sequence of moves that will traverse through every possible configuration of a Rubik's cube then take you back to whereveryou started. One of those states is the solved state. Meaning whenever you complete this sequence you will have done a full loop of all possible cube states.
The interesting thing is that it doesn't matter where you start, you can follow this same sequence. So you can be blindfolded, never see the cube, perform the sequence and one of those states will be a solved Rubik's cube.
That I believe is OPs point.
- sebastianmestre 2y agoYeah I got that, but it's really not as interesting as it seems. Let me explain why. Say we have an array p[1], p[2], ..., p[n] with all possible rubiks cube configurations Then this function will solve the cube: move(1) = p[1]^(-1) move(i) = p[i]^(-1) * p[i-1] In laymans terms, the resulting algorithm is: assume the initial configuration is p[1], then solve it. If it wasn't, undo those moves then solve as if the initial position was p[2], etc... So, yeah. Those fixed solving sequences / hamiltonian paths are actually very common. We can make one for any permutation of the group elements. So I posed a more interesting question: what is the simplest sequence of moves that has this property?