Square-field multi-turn walk from the center: Raj starts at the center, walks diagonally to North-East, turns right to the far edge, turns right and walks, midway turns right and walks, halfway turns left and reaches a new far edge. In what direction is Raj now?

Introduction / Context:
This stylized puzzle uses a square with Raj beginning at the center. Turning “right” means a 90° clockwise change relative to his current heading; “left” is 90° counter-clockwise. “Far end” indicates reaching a boundary.

Given Data / Assumptions:

• Start heading North-East from center along the main diagonal.
• First right from NE ⇒ South-East to the East boundary.
• Second right from SE ⇒ South-West direction along the interior.
• Midway right from SW ⇒ North-West.
• Halfway left from NW ⇒ South-West to a new far edge.

Concept / Approach:
Model headings as vectors: NE (1,1), SE (1,−1), SW (−1,−1), NW (−1,1). Apply right/left rotations in sequence and interpret “far end”/“midway”/“halfway” as traveling along those headings until boundary or stated fraction—directional heading is unaffected by distance.

Step-by-Step Solution:

Verification / Alternative check:
Track only headings; each right/left rotates by 90°, ending on SW.

Why Other Options Are Wrong:
North/North-West/South imply different net rotations.

Common Pitfalls:
Confusing “far end” with corners affecting heading; only turns change direction.

Final Answer:
South-West