Read the following information carefully and answer the questions given 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 one box is kept between box E and box G. Box I is kept three boxes above box G. Box E is kept four boxes below box H. As many boxes are kept between box H and box I as between box D and box E. Box E is kept above box D. Box F is kept immediately below box C. Only two boxes are kept between box A and box F. Box B is kept above box A.

Which among the following statement(s) is/are true?
I. More than four boxes are kept below box C
II. Box G is not kept below box H
III. Box B is kept at the topmost position

To determine the correct statements, we can step-by-step construct the arrangement of the nine boxes in a stack from top (9) to bottom (1).

Step 1: Analyze the clues related to H, I, G, E, and D.
1. Box $I$ is kept three boxes above box $G$. This means:
$I=G+3$ (with 2 boxes between them).
2. Only one box is kept between box $E$ and box $G$. This gives two possible relative placements for $E$:
- Case A: $E$ is below $G$ ($E=G-2$)
- Case B: $E$ is above $G$ ($E=G+2$)
3. Box $E$ is kept four boxes below box $H$. This means:
$H=E+4$ (with 3 boxes between them).

Step 2: Compare the number of boxes between H & I and D & E.
We are given: "As many boxes are kept between box $H$ and box $I$ as between box $D$ and box $E$." Also, box $E$ is kept above box $D$.
Let us evaluate Case B where $E=G+2$:
- Let $G$ be at position 2.
- Then $E=2+2=4$.
- $I=2+3=5$.
- $H=4+4=8$.
- The number of boxes between $H$ (8) and $I$ (5) is 2 (positions 6 and 7).
- Therefore, there must be 2 boxes between $D$ and $E$ (4). Since $E$ is above $D$, $D$ must be at position 1 (leaving positions 2 and 3 between them).
This gives us the relative sequence:
8: $H$
7: [empty]
6: [empty]
5: $I$
4: $E$
3: [empty]
2: $G$
1: $D$
Since there are 9 boxes, there is one more position left at either the top (9) or bottom (0). Let's assume the stack is from position 9 (top) to 1 (bottom), leaving position 9 vacant.

Step 3: Place the remaining boxes A, B, C, and F.
1. Box $F$ is kept immediately below box $C$. The only consecutive vacant positions available are 7 and 6.
- Position 7: $C$
- Position 6: $F$
2. Only two boxes are kept between box $A$ and box $F$. Since $F$ is at position 6, $A$ must be at position 3 (leaving positions 4 and 5 between them).
3. Box $B$ is kept above box $A$. The only remaining vacant position is 9, which is indeed above position 3. So, $B$ is at position 9.

Final Arrangement (from top to bottom):
9: $B$
8: $H$
7: $C$
6: $F$
5: $I$
4: $E$
3: $A$
2: $G$
1: $D$

Step 4: Verify the statements based on the final arrangement.
- Statement I: More than four boxes are kept below box C.
Box $C$ is at position 7, so there are 6 boxes ($F,I,E,A,G,D$) below it. This is more than four. (True)
- Statement II: Box G is not kept below box H.
Box $G$ is at position 2 and Box $H$ is at position 8, which means $G$ is kept below $H$. (False)
- Statement III: Box B is kept at the topmost position.
Box $B$ is at position 9, which is the topmost position. (True)

Therefore, both statement I and statement III are true.