A man is facing towards the east. He then turns 270 degrees in the clockwise direction and after that takes a right turn. Finally, he turns 90 degrees in the anti clockwise direction. After performing all these turns, which direction is he facing now?

Introduction / Context:
This problem deals purely with rotations and asks for the final facing direction of a man after several turns. He starts by facing east, then turns through a large clockwise angle, takes a right turn, and finally turns anti clockwise. Such questions test clarity about clockwise versus anti clockwise direction and how right and left turns relate to current orientation.

Given Data / Assumptions:

• The man initially faces east.
• He turns 270 degrees clockwise.
• Then he takes a right turn.
• Finally, he turns 90 degrees anti clockwise.
• We consider the basic compass directions: north, east, south, and west spaced at 90 degree intervals.

Concept / Approach:
A simple and reliable method is to track the direction after each turn rather than trying to combine all angles at once. A 270 degree clockwise turn is equivalent to a 90 degree anti clockwise turn, because both leave the person in the same direction relative to the start. After this, a right turn means another 90 degree clockwise rotation from the current facing direction. Finally, we subtract 90 degrees for the anti clockwise turn and see where we end up on the compass.

Step-by-Step Solution:
Step 1: The man begins facing east.Step 2: A 270 degree clockwise turn from east is the same as a 90 degree anti clockwise turn. Starting from east, a 90 degree anti clockwise turn leads to north.Step 3: Now he is facing north. A right turn from north is a 90 degree clockwise turn, which leads to east.Step 4: After this right turn, he is facing east again.Step 5: Finally, he turns 90 degrees anti clockwise from east, which leads back to north.Step 6: Therefore, after all rotations and turns, he is facing north.

Verification / Alternative check:
We can represent directions as angles on a circle: east as 90 degrees, south as 180 degrees, west as 270 degrees, and north as 0 or 360 degrees. Starting from east at 90 degrees, adding 270 degrees clockwise gives 360 degrees, which is equivalent to north. A right turn from north adds 90 degrees and returns to east at 90 degrees. Subtracting 90 degrees for the anti clockwise final turn brings us back to 0 degrees, or north. This angle based check agrees entirely with the stepwise direction tracking.

Why Other Options Are Wrong:
West would be correct if there were an extra 90 degree clockwise turn after the last step, but that is not described. South would require the final total rotation to land at 180 degrees, which does not happen. Remaining in east would only occur if the final anti clockwise turn were not made. South east is a diagonal direction and is not reachable through these exact quarter turns. Therefore, only north matches the combined effect of all the given rotations.

Common Pitfalls:
Many candidates misinterpret the 270 degree clockwise turn as leading directly to south because they mistakenly subtract 90 degrees instead of adding 270 to the initial angle. Others lose track of the orientation after the right turn and apply the last 90 degree anti clockwise rotation from the wrong starting direction. Drawing a compass and marking each step carefully avoids such confusion.

Final Answer:
After completing all the described turns, the man is facing towards the North.