Logs: liberachat/#haskell
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| 2026-01-07 02:40:14 | <haskellbridge> | <Liamzee> apparently i have no ability to assess whether DS claiming that there exists a odd move (quarter turn only) sequence that returns an edge piece to its starting location without flipping its colors |
| 2026-01-07 02:40:35 | <haskellbridge> | <Liamzee> is hallucination or not |
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| 2026-01-07 02:49:40 | <mange> | I don't think there is. 3x3 cubes have edge parity, from memory, so I think only even permutations bring them back. (The above linked Wikipedia page says that corners are in Z_3 and edges are in Z_2, which is consistent with my memory.) |
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| 2026-01-07 03:00:29 | <ncf> | "quarter turn only"? quarter turns generate all moves, what do you mean? |
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| 2026-01-07 03:20:02 | <int-e> | ncf: disallowing half turns matters if you're concerned with the number of moves you make, or just their parity, because each quarter turn is an odd permutation of the edge pieces and also an odd permutation of the corner pieces |
| 2026-01-07 03:20:59 | <int-e> | (when looking at piece positions, not their orientation) |
| 2026-01-07 03:22:37 | <ncf> | so an "odd move" is an odd number of quarter turns? |
| 2026-01-07 03:23:07 | <int-e> | "odd move sequence" |
| 2026-01-07 03:23:21 | <int-e> | it could certainly be phrased better |
| 2026-01-07 03:23:39 | <ncf> | oh |
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| 2026-01-07 03:24:02 | <ncf> | yeah i totally failed to parse that |
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| 2026-01-07 03:26:09 | <ncf> | the question has a bit of a trivial answer then: a single quarter move leaves 8 edges alone |
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| 2026-01-07 03:29:56 | <ncf> | requiring the edge to have moved during the sequence doesn't change anything, because you can always compose with Xⁿ, where X is a move of order n that moves every edge |
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| 2026-01-07 03:32:23 | <ncf> | if you want *every* quarter turn in the sequence to move the chosen edge, then the answer should be no because every quarter turn flips the edge's orientation |
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