Talk:Megaminx

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[edit] Contradictory?

The article claims that in the 6-coloured version, the visually-identical pairs cannot be physically interchanged. This means that in the 12-coloured version, not every possible arrangement of faces is possible. Therefore the number of possible combinations for the 6-coloured and 12-coloured version should be equal. This is just based on my intuition, so I could be wrong ;) --Cornflake pirate 13:03, 1 March 2007 (UTC)

Also, the end section about the permutations says that the 6 color and 12 color have different amounts of permutations, but with the same amount of pieces it realistically should be the same. if it is impossible to interchange the 2 colors on a given face, then these numbers should be the same, am I wrong?

Obviously there are the same number of pieces, no matter how they are identified. What counts as far as visible permutations are concerned is whether you can tell one state from another. If you can't tell them apart, they count as one permutation.

Taking a solved 6-colour puzzle and interchanging 1 pair of identically coloured pieces and then another pair so the puzzle is again in a solved state does not count as a separate permutation since the two states cannot be told apart unless you specifically identify each pair of like-pieces (they don't need to be marked with a pen - keeping track of each one is enough to uniquely identify it). There are no identically-coloured pieces on the 12-colour puzzle so every possible physical permutation counts.

To clarify - if I coloured all the faces blue so that there were 30 identically-coloured edge pieces (and 20 corners) there would only be one permutation since rearranging the puzzle would make no discernible difference. I'll remove the Contradiction Template if no-one has any objections. Secret Squïrrel 14:36, 25 March 2007 (UTC)