If South-East becomes North, which direction will West become?

Concept

When one compass direction is renamed to another, the whole eight-point compass — N, NE, E, SE, S, SW, W, NW, arranged in a clockwise ring — has been rotated by one fixed angle. The very same rotation, applied to any other direction on the ring, gives its new name.

Application

1. List the eight directions in their natural clockwise order: N, NE, E, SE, S, SW, W, NW.

2. South-East is renamed North. Moving from South-East to North against the clockwise order — SE, then E, then NE, then N — takes three 45° steps, so the whole ring has rotated 135° anticlockwise.

3. Apply that same 135° (three-step) anticlockwise shift to West. Moving anticlockwise from West — W, then SW, then S, then SE — also takes three steps and lands on South-East.

Cross-check

Re-run the same three-step anticlockwise shift on the original pair as a check: South-East, East, North-East, North — three steps, ending exactly at North, which matches the given fact. Since the shift checks out, the identical shift applied to West is valid, so West becomes South-East.