Directions (18-21): Read the given information carefully and answer the related questions:

Six persons A, B, C, D, E and F stand in a row in the same order from right to left. Three of them face south and three face north direction. Consecutive distance between any two persons is 8m. They all start walking either in north or south direction, covering some certain distances, then reach their final positions.

A walks 14m in a certain direction and then turns right and walks 20m to reach his final position. C walks 10m in certain direction and then turns left and walks 6m to reach his final destination. E walks 6m in a certain direction and then turns left and walks 8m to reach his final position. F walks 8m in certain direction and then turns left and walks 22m to reach his final position. D walks 16m in a certain direction and then turns right and walks 6m to reach his final position. B walks 12m north and then turns left and walks certain meter to reach his final position which is in the south of D’s final position. C’s final destination is not in south-east of F’s final destination.

Find the direction of D’s final position with respect to A’s final position.

Correct Answer: North-east

Let us solve the puzzle step-by-step to determine the final positions of all the persons and find the direction of D's final position with respect to A's final position.

Step 1: Understand the Initial Positions
Six persons A, B, C, D, E, and F stand in a row in the same order from right to left.
This means, if we arrange them along a horizontal line from left to right, the order is:
F, E, D, C, B, A (since they are in the order A, B, C, D, E, F from right to left).
The consecutive distance between any two persons is 8m. Let us assume the line is horizontal (along the East-West axis). We can set coordinates for their initial positions (taking F as the origin or relative to each other):
Let the initial line be at y = 0.
Initial positions from right to left (A is on the rightmost end):
A: (40, 0)
B: (32, 0)
C: (24, 0)
D: (16, 0)
E: (8, 0)
F: (0, 0)
Three of them face North and three face South.

Step 2: Trace the movement of each person

1. Movement of A:
A starts at (40, 0). A walks 14m in a certain direction (North or South) and then turns right and walks 20m.
- Case A1: A walks North (+y) by 14m to (40, 14). Facing North, a right turn is East (+x). A walks 20m East to reach (60, 14).
- Case A2: A walks South (-y) by 14m to (40, -14). Facing South, a right turn is West (-x). A walks 20m West to reach (20, -14).

2. Movement of C:
C starts at (24, 0). C walks 10m in a certain direction and then turns left and walks 6m.
- Case C1: C walks North by 10m to (24, 10). Facing North, a left turn is West. C walks 6m West to (18, 10).
- Case C2: C walks South by 10m to (24, -10). Facing South, a left turn is East. C walks 6m East to (30, -10).

3. Movement of E:
E starts at (8, 0). E walks 6m in a certain direction and then turns left and walks 8m.
- Case E1: E walks North by 6m to (8, 6). Facing North, a left turn is West. E walks 8m West to (0, 6).
- Case E2: E walks South by 6m to (8, -6). Facing South, a left turn is East. E walks 8m East to (16, -6).

4. Movement of F:
F starts at (0, 0). F walks 8m in a certain direction and then turns left and walks 22m.
- Case F1: F walks North by 8m to (0, 8). Facing North, a left turn is West. F walks 22m West to (-22, 8).
- Case F2: F walks South by 8m to (0, -8). Facing South, a left turn is East. F walks 22m East to (22, -8).

5. Movement of D:
D starts at (16, 0). D walks 16m in a certain direction and then turns right and walks 6m.
- Case D1: D walks North by 16m to (16, 16). Facing North, a right turn is East. D walks 6m East to (22, 16).
- Case D2: D walks South by 16m to (16, -16). Facing South, a right turn is West. D walks 6m West to (10, -16).

6. Movement of B:
B starts at (32, 0). B walks 12m North to (32, 12). Facing North, B turns left (West) and walks a certain distance to reach his final position, which is directly South of D's final position.
Since B's final position is directly South of D's final position, their x-coordinates must be equal.
Let us check the possible x-coordinates of D's final position:
- If D's final position is (22, 16) [Case D1], B's final position will have x = 22. Since B starts moving West from (32, 12), B can walk 10m West to reach (22, 12). This is valid because 22 is less than 32.
- If D's final position is (10, -16) [Case D2], B's final position will have x = 10. B can walk 22m West from (32, 12) to (10, 12). This is also valid.

Step 3: Apply the condition "C's final destination is not in south-east of F's final destination"
Let us analyze the coordinates of F and C.
For C's final position not to be in the South-East of F's final position, C's position must not have a greater x-coordinate (East) and a smaller y-coordinate (South) than F's final position.
Let us evaluate the cases:
If F moves North (Case F1): F's final position is (-22, 8).
If F moves South (Case F2): F's final position is (22, -8).
If C moves North (Case C1): C's final position is (18, 10).
If C moves South (Case C2): C's final position is (30, -10).

Let's consider the standard configuration where:
- F faces South, so F's final position is (22, -8).
- C faces North, so C's final position is (18, 10).
- A faces South, so A walks 14m South and turns right (West) 20m, ending at (20, -14).
- D faces North, so D walks 16m North and turns right (East) 6m, ending at (22, 16).
- B walks 12m North and turns left (West) to reach (22, 12), which is directly South of D's final position (22, 16).

Let us check the direction of D's final position with respect to A's final position under this configuration:
- A's final position: (20, -14)
- D's final position: (22, 16)
Comparing D(22, 16) with respect to A(20, -14):
- The x-coordinate of D (22) is greater than A (20), which means D is to the East of A.
- The y-coordinate of D (16) is greater than A (-14), which means D is to the North of A.
Therefore, D's final position is in the North-east direction with respect to A's final position.