Question Statement:
Six agricultural scientists ($A, B, C, D, E, F$) are seated around a circular conference table facing inward toward the center at equal angular spacings. It is given that:
1. $A$ sits directly opposite $D$.
2. $B$ sits to the immediate right of $A$.
3. $C$ sits between $A$ and $E$.
Who sits to the immediate left of $D$? Let scientists $A, B, C, D, E, F$ be mapped to integers $1, 2, 3, 4, 5, 6$, respectively. Enter the corresponding integer of the scientist seated to the immediate left of $D$: ________ (answer in integer).
Step-by-Step Solution & Explanation
**Method 1: Circular Seating Deduction**
Assign 6 clockwise positions $1$ to $6$ around the circle:
- Let $A$ be at position 1.
- Since $D$ is opposite $A$, $D$ is at position 4.
- $B$ is to the immediate right of $A$ (counter-clockwise neighbor when facing center), placing $B$ at position 6.
- $C$ is between $A$ and $E$. The available neighbor of $A$ is position 2 (clockwise), so $C$ is at position 2 and $E$ is at position 3.
- The remaining position 5 must be occupied by $F$.
At seat 4 ($D$), facing the center:
- Looking inward, the immediate left is the clockwise neighbor (position 5), which is occupied by $F$.
$F$ corresponds to integer $6$.