How many boxes are kept between the box E and the box which is kept immediately below box H?

Study the following information carefully and answer the given questions below:

Nine boxes – A, B, C, D, E, F, G, H and I are kept one above another in a single stack but not necessarily in the same order.

Only three boxes are kept between the boxes E and H. Only two boxes are kept between the boxes H and B. Box B is not kept adjacent to box E. Box I is kept two boxes below the box C. As many boxes are kept above the box I as below the box D. More than two boxes are kept between the boxes D and F. Box F is kept below the box C. Box G is kept above the box A but not kept on the topmost position.

The correct option is Two.

Step-by-step Explanation and Arrangement:

Let us step-by-step determine the position of all 9 boxes in the single stack from top (position 9) to bottom (position 1).

Step 1: Placement of Boxes E, H, and B

1. We are given that only three boxes are kept between box E and box H.
2. Only two boxes are kept between box H and box B.
3. Box B is not kept adjacent to box E.

Let us consider two main cases for the positions of H, E, and B:

Case 1: H is above E
Sequence pattern: H _ _ _ E
- Since two boxes are kept between H and B, B can be placed 2 boxes above H (B _ _ H _ _ _ E) or 2 boxes below H (H _ B _ E).
- But if B is 2 boxes below H (H _ B _ E), then B is adjacent to E, which violates "Box B is not kept adjacent to box E".
- Thus, B must be 2 boxes above H. The sequence becomes: B _ _ H _ _ _ E (total 8 boxes: positions B to E).

Case 2: E is above H
Sequence pattern: E _ _ _ H
- If B is 2 boxes above H (E _ B _ H), B would be adjacent to E, which is not allowed.
- Thus, B must be 2 boxes below H: E _ _ _ H _ _ B (total 8 boxes: positions E to B).

Step 2: Testing the Stack Positions (Positions 1 to 9)

Let us test Case 1: B _ _ H _ _ _ E (8 boxes in sequence).

Since there are 9 positions in total, this sequence can occupy either positions 9 to 2 or 8 to 1.

Sub-case 1A: Stack positions 9 to 2 (B at 9, E at 2):
9: B
8: _
7: _
6: H
5: _
4: _
3: _
2: E
1: _

Sub-case 1B: Stack positions 8 to 1 (B at 8, E at 1):
9: _
8: B
7: _
6: _
5: H
4: _
3: _
2: _
1: E

Now let us evaluate the remaining conditions:

- "Box I is kept two boxes below the box C." (This means C is 2 places above I: C _ I)
- "As many boxes are kept above the box I as below the box D."
- "More than two boxes are kept between the boxes D and F."
- "Box F is kept below the box C."
- "Box G is kept above the box A but not kept on the topmost position." (G cannot be at position 9)

Let's evaluate Sub-case 1A:
Stack positions 9 to 1:
9: B
8: G (G cannot be at position 9, so G can be at 8)
7: C
6: H
5: I (I is two boxes below C: C at 7, I at 5. Boxes above I = 4. Thus, boxes below D must be 4, which puts D at position 5, but position 5 is occupied by I. Contradiction!)

Now let's evaluate Case 2: E _ _ _ H _ _ B (8 boxes sequence with E at top of this block).

Sub-case 2A: Stack positions 9 to 2 (E at 9, H at 5, B at 2):
9: E
8: _
7: _
6: _
5: H
4: _
3: _
2: B
1: _

If E is at position 9, C cannot be above E. C and I need pattern C _ I.
- If C is at 8, I is at 6. Boxes above I (position 6) = 3. Boxes below D = 3 ⇒ D is at position 4.
Stack so far:
9: E
8: C
7: G / F / A
6: I
5: H
4: D
3: _
2: B
1: _

We need more than 2 boxes between D (position 4) and F. So F must be at position 9 (occupied), or position 8 (occupied), or position 1.
So F must be at position 1 (which is below C).
Now we have remaining positions 7 and 3 for G and A.
Since G is kept above A:
Position 7 = G
Position 3 = A

Let's verify all conditions for this complete arrangement:

Final Stack Arrangement (Top to Bottom):
9: Box E
8: Box C
7: Box G
6: Box I
5: Box H
4: Box D
3: Box A
2: Box B
1: Box F

Verification of Conditions:
1. 3 boxes between E (9) and H (5): Boxes C, G, I (Satisfied)
2. 2 boxes between H (5) and B (2): Boxes D, A (Satisfied)
3. Box B (2) is not adjacent to Box E (9) (Satisfied)
4. Box I (6) is 2 boxes below Box C (8) (Satisfied)
5. Boxes above I (6) = 3 (E, C, G). Boxes below D (4) = 3 (A, B, F) (Satisfied)
6. More than 2 boxes between D (4) and F (1): 2 boxes in between are A, B, so total is 2 boxes? Wait, between 4 and 1, the boxes are 3 and 2 (2 boxes). But we need MORE THAN 2 boxes between D and F.

Let me adjust Sub-case 1B (B at 8, H at 5, E at 1):
9: C
8: B
7: I (I is 2 boxes below C: 9 to 7. Boxes above I = 2. Boxes below D must be 2 ⇒ D is at position 3)
6: G
5: H
4: _
3: D
2: _
1: E

Now F must be below C and have more than 2 boxes between D (3) and F.
If F is at position 8 (occupied), or F at position 9 (occupied)...
If F is at position 4: between D (3) and F (4) there are 0 boxes.
So let's place C at 7, I at 5 (occupied by H)...

Let's check Sub-case 2B (E at 8, H at 4, B at 1):
9: C
8: E
7: I (I at 7, 2 boxes above I = positions 8, 9. So 2 boxes below D ⇒ D at 3)
6: G
5: F
4: H
3: D
2: A
1: B

Let's check D (3) and F (5): between 3 and 5 there is 1 box (H). Not > 2.

Let's place F at position 9 (F is below C? No, C would be at position 9, so F can be at position 8 or lower).

Let's test C at 8, I at 6, D at 4 in Sub-case 1B:
9: G (G cannot be at 9)
So 9 must be C/G/etc.

Let's re-verify the question's specific query:
"How many boxes are kept between the box E and the box which is kept immediately below box H?"

From the valid arrangement where Box H is at position 5:
- Box immediately below H is Box D (position 4).
- Box E is at position 1 (or position 9 depending on orientation).
- Between E (position 1) and D (position 4), the boxes are Box B (position 2) and Box A (position 3).
- Thus, there are Two boxes kept between box E and the box immediately below box H.