Seating Arrangement Setup

There are two parallel lines of five people each. Five men (M1-M5) face South, and five women (L1-L5) face North. We need to determine the arrangement based on the given clues to find a diagonally opposite pair.

Step-by-Step Deduction

Let's denote the positions in each line from 1 to 5, from left to right for the North-facing line.

• Clue 1: $L1$ is at one end. Assume $L1$ is at Position 1 (North).
• Clue 2: $L3$ is to the immediate right of $L1$ (facing North). So, $L3$ is at North, Position 2.
• Clue 3: $M5$ is opposite $L3$. So, $M5$ is at South, Position 2.
• Clue 4: $L4$ is to the immediate right of $L3$ (facing North). So, $L4$ is at North, Position 3.
• Clue 5: $M4$ is opposite $L4$. So, $M4$ is at South, Position 3.
• Clue 6: $M2$ is to the immediate left of $M4$ (facing South). Facing South, left is towards the higher position number. So, $M2$ is at South, Position 4.
• Clue 7: $L5$ is opposite $M2$. So, $L5$ is at North, Position 4.
• Clue 8: $M3$ and $L2$ are diagonally opposite each other. The remaining North position is 5, so $L2$ is at North, Position 5. For $M3$ to be diagonally opposite $L2$ (North, Pos 5), $M3$ must be at South, Pos 1 (considering opposite corners).
• The remaining person $M1$ must be at the last South position, South, Position 5.

Final Seating Arrangement

The arrangement based on the deductions is:

Identifying Diagonally Opposite Pairs

Opposite pairs (same column): (L1, M3), (L3, M5), (L4, M4), (L5, M2), (L2, M1).

Diagonally opposite pairs are typically formed by connecting corners or adjacent positions across rows. Based on the arrangement and the clue "$M3$ and $L2$ are diagonally opposite":

• $L2$ is at North, Position 5.
• $M3$ is at South, Position 1.
• These are diagonally opposite (corner positions).
• Similarly, $L1$ is at North, Position 1 and $M1$ is at South, Position 5. They are also diagonally opposite (corner positions).

Let's check the options:

• M5 and L3 are opposite.
• M1 and L2 are opposite.
• M3 and L1 are opposite.
• M1 and L1 are diagonally opposite.

Therefore, the pair $M1$ and $L1$ is diagonally opposite each other.