It seems well-established that combinations of more than just two dyes are supported:
Light Grey = Grey + White = (Black + White) + White
Magenta = Pink + Purple = Pink + (Red + Blue)
Magenta = Pink + Purple = (Red + White) + (Red + Blue)
Since these are existing recipes:
Magenta = Pink + Purple = (Red + White) + (Red + Blue)
Purple = Red + Blue
The recipe for Magenta = (Red + White) + Purple can be considered missing.
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Comments 20
The point is that there is a recipe that logically should work but it's missing from the game. There's no reason for Red + Blue + Red + White to make Magenta, and Pink + Red + Blue to make Magenta, and Pink + Purple to make Magenta, but not Purple + Red + White.
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All recipes work as intended.
List of recipes: http://minecraft.gamepedia.com/Magenta_Dye