Directions (14-15): Study the information carefully and answer the questions given below.

Five boxes are placed one above the other in a stack. Box A is placed adjacent to box D. Box E is placed above box C but not on the topmost position. Box D is not placed adjacent to box B. If box F is added to the stack, then the box F is placed below the box B. All the boxes contain different numbers of pencils in a consecutive multiple of 6 from bottom to top. Box A contains 36 pencils and does not place at odd numbered position when counts from the top. More than two boxes are placed above the box D. Total number of pencils is not more than 198. Neither box E nor box F is kept adjacent to box D.

How many boxes are placed between box D and box B?

To find the number of boxes between box D and box B, we can analyze the given constraints step-by-step to determine the unique vertical arrangement of the five boxes (A, B, C, D, and E) from top to bottom (1st to 5th):

1. Analyze the position of Box D:
According to the clue, "More than two boxes are placed above the box D." In a stack of 5 boxes, this means Box D must be either at the 4th or 5th position from the top.

2. Analyze the position of Box A:
We are told that "Box A is placed adjacent to box D" and "does not place at odd numbered position when counts from the top." Thus, Box A must occupy an even-numbered position (either the 2nd or 4th position from the top).
- If Box D were at the 5th position, Box A (being adjacent) would have to be at the 4th position (even position, which is possible).
- If Box D is at the 4th position, Box A (being adjacent) can be at the 3rd position (odd position, which is not possible) or the 5th position (odd position, which is not possible).
Thus, to satisfy the constraints, Box D is placed at the 4th position and Box A is placed at the 3rd position. This satisfies the condition that more than two boxes (1st, 2nd, and 3rd) are above Box D.

3. Determine the positions of the remaining boxes (B, C, and E):
We have positions 1st, 2nd, and 5th remaining for boxes B, C, and E.
- "Box E is placed above box C but not on the topmost position (1st)." This means Box E must be placed at the 2nd position, and Box C must be placed at the 5th position (bottommost).
- This leaves the 1st position (topmost) for Box B.

4. Final Stack Arrangement:
The final stack arrangement from top to bottom is:
- 1st (Top): Box B
- 2nd: Box E
- 3rd: Box A
- 4th: Box D
- 5th (Bottom): Box C

5. Verify the remaining conditions:
- Box D (4th) is not adjacent to Box B (1st): True.
- Neither Box E (2nd) nor Box F (placed below B) is adjacent to Box D (4th): True.
- Counting the boxes between Box D (4th) and Box B (1st), we find Box E (2nd) and Box A (3rd).

Therefore, there are exactly Two boxes placed between Box D and Box B.