How many boxes are kept between E and box number 4?

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Accepted Answer

Step-by-step reasoning:

1. Number 12 must be immediately above E, and E is above number 9. Hence both 12 and E occupy two consecutive positions above 9, so 9 cannot be in the top two positions. Therefore the only feasible placement for number 9 (given there are 7 boxes) that allows two positions above it for $12\rightarrow E$ is position $3$. Thus positions $1$ and $2$ are $12$ and $E$ respectively, and position $3$ is $9$.

2. "Only three boxes are kept between G and box number 9" forces G to be at position $7$ (since $9$ is at $3$). "Only two boxes are kept between G and B" then places B at position $4$ (so $B$ is below $9$, satisfying that condition).

3. "Only one box is kept between B and box number 4" puts number $4$ at position $6$ (since B is at $4$).

4. E (position $2$) is not $7$ or $8$ and must satisfy: "There is only one box between E and the box having number less than E." If we set E = $5$ at position $2$, then the box with a number less than $5$ can be at position $4$ (one box between positions $2$ and $4$). So B at position $4$ must have number $2$.

5. Remaining numbers are $7$ and $8$ to place at positions $5$ and $7$. The clue "Only two boxes are kept between box number 5 and F" requires $F$ to be at position $5$ (since number $5$ is at position $2$), so $F$ occupies position $5$. The difference between $F$ and the box immediately below it (position $6$, number $4$) must be less than $4$, so $F$ must be $7$ (since $|7-4|=3<4$, while $|8-4|=4$ is not allowed). Thus position $5$ is $F(7)$ and position $7$ is $G(8)$.

6. Remaining boxes A and C (and D) must fill positions $1$, $3$, $6$. C is not topmost and C's number is not $4$, so C must be at position $3$ (number $9$). "Only two boxes are kept between C and A" places A at position $6$ (number $4$). The remaining position $1$ is D with number $12$.

7. Final arrangement (top to bottom):
   1: D(12)
   2: E(5)
   3: C(9)
   4: B(2)
   5: F(7)
   6: A(4)
   7: G(8)

8. How many boxes are between E (position $2$) and box number $4$ (position $6$)? The boxes between positions $2$ and $6$ are at positions $3$, $4$, and $5$ — three boxes.

FINAL_ANSWER: a

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