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How do I get a Redstone single to go up 3 block spaces?
It would have to somehow go up 3 blocks vertically.
or you can build a "vertical repeater" using RS torches.(if a one-tick delay doesn't mess up what your trying to do).
You're best bet in either case would be the staircase (after TU12 you can change the full blocks to upside-down slabs to make it more compact).