In the morning X and Y are walking towards each other in a park. When they meet, Y's shadow falls straight in front of X along the line joining them. In which direction is X facing?

Introduction / Context:
This question involves understanding the relationship between the sun's position, the direction of a person's shadow and the facing direction of another person. X and Y are walking towards each other in the morning, and Y's shadow falls straight in front of X. We must deduce X's facing direction using basic facts about how shadows are cast.

Given Data / Assumptions:
- It is morning, so the sun is in the eastern part of the sky. - X and Y are walking towards each other along a straight path in a park. - When they meet, Y's shadow falls straight in front of X along the same line on which they are walking. - Shadows are cast in the direction opposite to the sun.

Concept / Approach:
In the morning the sun is roughly in the east, so shadows fall towards the west. If Y's shadow falls straight in front of X, that means the line from Y to the tip of Y's shadow runs directly towards X. Therefore, X must be located in the direction where Y's shadow points. Since Y's shadow points west in the morning, X must be to the west of Y when they meet. Because they are walking towards each other, X must be facing east and Y must be facing west at the moment of meeting.

Step-by-Step Solution:
1. In the morning, the sun is in the east, so for any standing person, the shadow will fall towards the west. 2. At the moment X and Y meet, Y's shadow is said to fall straight in front of X along the line on which they are walking. 3. This means that from Y, the direction of the shadow passes through X or lies directly between Y and X. 4. Because the shadow points west, X must be towards the west of Y, standing on the same line. 5. Since X and Y are walking towards each other, if X is to the west of Y, X must be facing east and Y must be facing west. 6. Therefore, X is facing east at the time when Y's shadow falls straight in front of him.

Verification / Alternative check:
Visualize a straight path running east to west. Place X at a point on the west side and Y at a point on the east side, walking towards each other. In the morning, light travels from east to west, so Y's shadow extends behind him towards the west, that is, towards X. When they meet, Y's shadow falls between Y and X, effectively in front of X as he looks eastwards. Trying the opposite configuration, with X on the east and Y on the west, would produce shadows pointing away from X rather than towards him, so that setup does not satisfy the problem statement.

Why Other Options Are Wrong:
- South or North do not align with the east to west shadow pattern in the morning. - West would place X facing towards the west, making it impossible for Y's westward shadow to fall in front of him along the line of approach. - North East is a diagonal direction that does not fit the simple east west shadow logic provided.

Common Pitfalls:
Examinees sometimes mix up the sun's position at different times of day, or they imagine shadows incorrectly. Remembering that in the morning the sun is in the east and shadows fall towards the west is crucial. Another pitfall is forgetting that they are walking towards each other, which constrains their relative positions on the line. Ensuring consistency between the movement direction and the shadow direction avoids wrong conclusions.

Final Answer:
X is facing east.