Analyze the given information thoroughly and answer the following question.
Eight students, A, B, C, D, E, F, G, and H, sit in a row such that some face North and others face South. No three consecutive students face the same direction. A sits at the extreme left end of the row. F sits second to the left of H, who faces North. Four students sit between B and G, and G faces North. D sits second to the right of B. C sits adjacent to B and faces South. E sits to the immediate right of F.
How many students face the south direction?
Correct Answer :
Four
Solution :
The correct option is Four.
Let's determine the positions and facing directions of all eight students (numbered 1 to 8 from left to right) step-by-step based on the given clues:
1. Total seats and constraint:
There are 8 seats: 1, 2, 3, 4, 5, 6, 7, 8 from left to right.
No three consecutive students face the same direction.
2. Position of A:
A sits at the extreme left end of the row.
So, Position 1 = A.
3. Positions of B and G:
Four students sit between B and G, and G faces North (G → North).
The possible pairs of positions for (B, G) with 4 students between them are (2, 7) or (3, 8).
4. Position of D:
D sits second to the right of B.
If B is at Position 7, D would be at Position 5 (if B faces South) or 9 (impossible). But C sits adjacent to B and faces South. Let's analyze carefully:
If B is at Position 2:
D is second to the right of B, so D must be at Position 4 (if B faces South). [If B faces North, second to the right of B would be Position 0, which is impossible]. Therefore, B must face South, and D is at Position 4.
Then G (with 4 students between B and G) is at Position 7, and G faces North.
5. Position of C:
C sits adjacent to B and faces South.
Since B is at Position 2 and A is at Position 1, C must be at Position 3.
So: Position 1 = A, Position 2 = B (South), Position 3 = C (South), Position 4 = D, Position 7 = G (North).
6. Positions of H, F, and E:
Remaining available positions are 5, 6, and 8.
F sits second to the left of H, who faces North (H → North).
Since H faces North, left of H means towards the left (smaller position numbers).
If H is at Position 8 (facing North), second to the left of H is Position 6. So F is at Position 6.
E sits to the immediate right of F.
Since Position 5 is vacant, E must be at Position 5, which means the immediate right of F is Position 5, so F must face South.
7. Complete arrangement of students:
Position 1: A
Position 2: B (South)
Position 3: C (South)
Position 4: D
Position 5: E
Position 6: F (South)
Position 7: G (North)
Position 8: H (North)
8. Determining facing directions for remaining students:
Constraint: No three consecutive students face the same direction.
Positions 2 and 3 (B and C) face South. Therefore, Position 1 (A) MUST face North (otherwise A, B, C would all face South).
Positions 7 and 8 (G and H) face North. Therefore, Position 6 (F) facing South is consistent, and Position 5 (E) sitting to the immediate right of F (facing South) puts E at Position 5.
Now, let's check D (Position 4) and E (Position 5):
D is second to the right of B (B is at 2, facing South, so 2 positions right of B is position 4). D faces South or North?
Since B (South) and C (South) face South, if D also faced South, then B, C, D would be three consecutive South. Thus, D MUST face North.
With D (North), G (North), H (North): if E also faced North, then D, E, G, H would have consecutive Norths. But for E at Position 5, to be to the immediate right of F (Position 6 facing South), E is at Position 5.
If E faces South, then the directions from position 1 to 8 are:
1 (A): North
2 (B): South
3 (C): South
4 (D): North
5 (E): South
6 (F): South
7 (G): North
8 (H): North
Let's verify no three consecutive students face the same direction:
Directions: N, S, S, N, S, S, N, N
At most 2 consecutive students face the same direction everywhere!
9. Counting students facing South:
Students facing South are B (2), C (3), E (5), and F (6).
Total facing South = 4 students.
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