Problem 5 - Entrance Test

Let's consider directions in degrees clockwise from North (0 degrees): North = 0/360, East = 90, South = 180, West = 270 North-East = 45, South-East = 135, South-West = 225, North-West = 315 1. South-East (135 degrees) becomes North (0 degrees). This is a 135-degree anti-clockwise rotation (135 - 135 = 0). Or a 225-degree clockwise rotation (135 + 225 = 360 = 0). 2. North-East (45 degrees) becomes West (270 degrees). This is a 45-degree anti-clockwise rotation (45-135 = -90, -90+360 = 270 degrees). This doesn't match a fixed rotation. Let's recheck the angles. North-East (45) to West (270) is 225 degrees anti-clockwise (270 - 45 = 225). Or 135 degrees clockwise (360 - 225 = 135 degrees clockwise, or 45 + 135 = 180 which is South. So 45 + X = 270, X = 225 clockwise. No, that's not right. 45 - X = 270. X = 45-270 = -225, so 225 degrees anti-clockwise). Let's assume a consistent anti-clockwise rotation: SE (135 deg) -> N (360 deg or 0 deg). Difference = 360 - 135 = 225 degrees anti-clockwise. NE (45 deg) -> W (270 deg). Difference = 270 - 45 = 225 degrees anti-clockwise. The rotation is 225 degrees anti-clockwise. Now apply this to East (90 degrees): 90 - 225 = -135 degrees. Adding 360 to get a positive angle: -135 + 360 = 225 degrees. 225 degrees corresponds to South-West. Alternatively, considering clockwise rotation: SE (135) to N (0/360) is a 225-degree clockwise rotation (360-135=225). NE (45) to W (270) is 225-degree clockwise rotation (45+225 = 270). So, it's a 225-degree clockwise rotation. East (90 degrees) + 225 degrees = 315 degrees. 315 degrees is North-West.