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Your primality test is beautiful.
equal parts impressed and furious
I think you've got it a little confused. Here is an excerpt from the Kata details:
In ["NORTH", "EAST", "WEST", "SOUTH", "WEST", "WEST"], "NORTH" and "SOUTH" are not directly opposite but they become directly opposite after the reduction of "EAST" and "WEST" so the whole path is reducible to ["WEST", "WEST"].
This seems to say that to 'reduce' two directions they must be consecutive. So your example, '['NORTH', 'WEST', 'SOUTH', 'EAST']', can't be reduced further. If it were N-S-W-E, it would reduce to [], but that's not how this Kata is set up.