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

Seven boxes- A, B, C, D, E, F and G are kept one above another in a single stack but not necessarily in the same order.
Only two boxes are kept between box A and box F. Box B is kept two boxes above box F. Only three boxes are kept between box B and box G. The number of boxes kept above box G is one more than the number of boxes kept below box C. Box D is kept two boxes below box C. Box E does not kept below box D.

How many boxes are kept between box E and box D?

To find the number of boxes kept between box E and box D, we can logically determine the arrangement of all seven boxes (A, B, C, D, E, F, and G) from top to bottom (positions 7 down to 1).

Let's analyze the given clues step-by-step:

1. Box B is kept two boxes above box F:
This means the relative position is: B, [empty space], F. If F is at position $x$, then B is at position $x+2$.

2. Only two boxes are kept between box A and box F:
This gives us two possibilities for the position of box A relative to F:
- Case 1: A is kept above F, so the order is A, [empty], [empty], F. Combining this with clue 1 (B is one box above the space above F), the arrangement would be A, B, [empty], F.
- Case 2: A is kept below F, so the order is F, [empty], [empty], A. Combining this with clue 1, the arrangement would be B, [empty], F, [empty], [empty], A.

3. Only three boxes are kept between box B and box G:
- Let's test Case 1: If the stack has A, B, [empty], F (occupying 4 positions):
If G is below B with 3 boxes between them: B, [empty], F, [empty], G. This structure (A, B, [empty], F, G) uses 5 positions. G is at the bottom, and B is at the second position from the top.
- Let's test Case 2: If the stack has B, [empty], F, [empty], [empty], A (occupying 6 positions):
If G is below B with 3 boxes between them, G must be at the position just below F. This gives: B, [empty], F, G, [empty], A (occupying 6 positions).

4. The number of boxes kept above box G is one more than the number of boxes kept below box C:
Let's represent this mathematically:
$\text{Boxes above G}=\text{Boxes below C}+1$
Let's place the configurations in the 7-position stack (where 7 is the top and 1 is the bottom):
Let's try the arrangement from Case 2: B (6th), [empty] (5th), F (4th), G (3rd), [empty] (2nd), A (1st).
If G is at position 3, the number of boxes above G is 4 (positions 4, 5, 6, 7).
Using our relation:
$4=\text{Boxes below C}+1$ ⇒ $\text{Boxes below C}=3$.
This means box C must be at position 4. But position 4 is already occupied by F. Thus, this arrangement is invalid.

Let's try Case 1's general layout: A, B, [empty], F, [empty], G.
Let's place B at position 6. Then F is at position 4, and G is at position 2 (since there are 3 boxes between B and G: positions 5, 4, and 3).
Since A is above B, and B is at 6, A must be at position 7. This fills positions:
Position 7: A
Position 6: B
Position 5: [empty]
Position 4: F
Position 3: [empty]
Position 2: G
Position 1: [empty]
Let's check the relation for G: G is at position 2, so there are 5 boxes above G (positions 3, 4, 5, 6, 7).
Using our relation:
$5=\text{Boxes below C}+1$ ⇒ $\text{Boxes below C}=4$.
This means box C must be at position 5 (so that positions 1, 2, 3, and 4 are below it).

5. Box D is kept two boxes below box C:
Since C is at position 5, box D must be two boxes below C, which is at position 3 (5 - 2 = 3). This is currently empty, so we can place D at position 3.

6. Box E does not kept below box D:
The remaining empty position is position 1. If E were at position 1, it would be below D (which is at position 3). Since E cannot be below D, E must be placed in a higher position. The current arrangement has:
Position 7: A
Position 6: B
Position 5: C
Position 4: F
Position 3: D
Position 2: G
Position 1: [empty]
Since all other positions are filled, let's re-evaluate the placement. What if B is at position 5?
If B is at position 5:
Then F is at position 3 (two boxes below B).
A must be at position 6 (two boxes above F).
G is at position 1 (three boxes between B and G: positions 4, 3, 2).
Let's check G: G is at position 1, so there are 6 boxes above G.
Using the relation:
$6=\text{Boxes below C}+1$ ⇒ $\text{Boxes below C}=5$.
This means C must be at position 6. But position 6 is already occupied by A. So this is invalid.

Let's try B at position 7:
F is at position 5.
A is at position 8 (not possible as there are only 7 boxes). If A is below F, then A is at position 2.
G is at position 3 (three boxes between B and G: positions 6, 5, 4).
Let's check G: G is at position 3, so there are 4 boxes above G.
$4=\text{Boxes below C}+1$ ⇒ $\text{Boxes below C}=3$.
This means C is at position 4.
Since D is two boxes below C, D is at position 2. But position 2 is occupied by A. So this is invalid.

Let's find the correct configuration. What if E is at the top? Let's check the placement:
Position 7: E
Position 6: B
Position 5: C
Position 4: F
Position 3: D
Position 2: G
Position 1: A
Let's verify all clues with this stack:
- Stack: 7-E, 6-B, 5-C, 4-F, 3-D, 2-G, 1-A.
- Two boxes between A (1) and F (4): Yes (G at 2, D at 3).
- B (6) is two boxes above F (4): Yes (C at 5 is between them).
- Three boxes between B (6) and G (2): Yes (C at 5, F at 4, D at 3 are between them).
- Boxes above G (2) is 5 (E, B, C, F, D). Boxes below C (5) is 4 (F, D, G, A). $5=4+1$: Yes.
- D (3) is two boxes below C (5): Yes (F at 4 is between them).
- E (7) is not below D (3): Yes, E is above D.
This configuration is fully consistent.

Now, let's count the boxes kept between box E (position 7) and box D (position 3):
The boxes between them are at positions 6, 5, and 4 (which are boxes B, C, and F).
Therefore, there are exactly three boxes kept between box E and box D.