A horse is initially facing north. It turns 90 degrees in the clockwise direction, then turns 180 degrees in the anti clockwise direction, and then turns another 90 degrees in the same anti clockwise direction. After performing all these turns, which direction is the horse facing now?

Introduction / Context:
This problem involves sequential rotations and asks for the final facing direction. The horse starts facing north and then rotates through several angles in clockwise and anti clockwise directions. These types of questions test the ability to track orientation changes and understand that clockwise and anti clockwise rotations have opposite effects on final direction.

Given Data / Assumptions:

• The horse begins facing north.
• It turns 90 degrees clockwise.
• Then it turns 180 degrees anti clockwise.
• Then it turns another 90 degrees in the same anti clockwise direction.
• We treat rotations in a full circle of 360 degrees with directions north, east, south, and west spaced 90 degrees apart.

Concept / Approach:
Instead of trying to visualise the horse turning physically, we can use angle measures on a circle. We choose a convention where north corresponds to 0 degrees, east to 90 degrees, south to 180 degrees, and west to 270 degrees. Clockwise rotation is treated as adding positive angles and anti clockwise as subtracting, or vice versa, as long as we remain consistent. The net effect of all rotations determines the final direction.

Step-by-Step Solution:
Step 1: Start with the horse facing north. Represent this as 0 degrees.Step 2: A 90 degree clockwise turn from north brings the horse to face east, which corresponds to 90 degrees.Step 3: Now a 180 degree anti clockwise turn from east subtracts 180 degrees, taking the horse from 90 degrees to −90 degrees, which is equivalent to 270 degrees and corresponds to west.Step 4: The horse then turns another 90 degrees anti clockwise. Subtracting 90 degrees from 270 degrees gives 180 degrees.Step 5: An orientation of 180 degrees corresponds to facing south.Step 6: Therefore, after all the turns, the horse is facing south.

Verification / Alternative check:
We can also track the directions without angles. From north, 90 degrees clockwise leads to east. From east, a 180 degree anti clockwise rotation takes us back through north to west. Finally, another 90 degree anti clockwise turn from west leads to south. Following the directions step by step confirms that the final facing direction is south, matching the angle based reasoning.

Why Other Options Are Wrong:
East would be correct if the final anti clockwise turn were not applied, because that was the direction after the first rotation. South west and south east are diagonal directions that require intermediate 45 degree rotations not specified here. North west would require ending 90 degrees away from north in the opposite direction, which does not match the combined rotations described. Only south fits the full sequence of 90 clockwise, 180 anti clockwise, and 90 anti clockwise rotations.

Common Pitfalls:
Students sometimes forget that clockwise and anti clockwise rotations have opposite signs and mistakenly add all angle values together without considering direction. Others stop tracking after the second rotation and ignore the last 90 degree turn. Using a rough sketch of a compass and marking each rotation one by one is a reliable way to avoid errors in such questions.

Final Answer:
After all the specified turns, the horse is facing towards the South.