A man is initially facing North-West. He turns 90 degrees in the clockwise direction, then 180 degrees in the anticlockwise direction and then another 90 degrees in the same (anticlockwise) direction. After these three turns, in which direction is he facing?

Introduction:
This question focuses purely on direction changes caused by clockwise and anticlockwise turns. The man starts facing one of the inter-cardinal directions (North-West) and then makes three successive rotations. We must keep track of his facing direction after each turn and finally identify the direction he faces after all the turns are complete.

Given Data / Assumptions:
• Initial facing direction: North-West.• First turn: 90 degrees clockwise.• Second turn: 180 degrees anticlockwise.• Third turn: 90 degrees in the same (anticlockwise) direction as the second turn.• We assume the standard eight directions spaced at 45 degree intervals: N, NE, E, SE, S, SW, W, NW.

Concept / Approach:
Each 45 degree step around the compass moves you to an adjacent direction. Since the turns are multiples of 90 degrees, each 90 degree rotation equals two 45 degree steps. It is convenient to imagine the directions arranged in a circle and to count steps clockwise or anticlockwise from the starting point. By updating the facing direction after each turn, we arrive at the final facing direction.

Step-by-Step Solution:
Step 1: List the eight directions clockwise: North, North-East, East, South-East, South, South-West, West, North-West.Step 2: The man starts facing North-West, which is the last direction in this list.Step 3: First turn: 90 degrees clockwise from North-West. Ninety degrees is two steps of 45 degrees. From North-West, one clockwise step goes to North, and the second step goes to North-East. So after the first turn he faces North-East.Step 4: Second turn: 180 degrees anticlockwise from North-East. One hundred eighty degrees equals four steps of 45 degrees. From North-East, going anticlockwise four steps leads to South-West.Step 5: Third turn: 90 degrees anticlockwise from South-West (same direction as the second turn). Ninety degrees equals two steps anticlockwise. From South-West, two anticlockwise steps move us to South-East.Step 6: Therefore, after all the turns, the man is facing South-East.

Verification / Alternative check:
We can double check by noting net rotation. The first turn is +90 degrees (clockwise). The second is −180 degrees (anticlockwise), and the third is −90 degrees (anticlockwise). The total rotation is +90 − 180 − 90 = −180 degrees relative to the starting direction (North-West). Turning 180 degrees anticlockwise from North-West leads directly to South-East, confirming our earlier step-by-step reasoning.

Why Other Options Are Wrong:
South and South-West both lie adjacent to South-East but require a different net rotation. East would be reached from North-West by a 135 degree clockwise rotation, which is not the net effect here. North is neither 180 degrees nor the described set of rotations away from North-West. Only South-East matches the cumulative 180 degree anticlockwise change.

Common Pitfalls:
Students sometimes mix up clockwise and anticlockwise directions, or they forget that the second and third turns are in the same anticlockwise direction. Others attempt to track only the net angle without checking it against intermediate orientations, leading to sign errors. Carefully counting 45 degree steps around a drawn compass diagram is a robust way to avoid mistakes.

Final Answer:
After all the turns, the man is facing towards the South-East direction.