Which of the following boxes is kept immediately above A?

Question

Accepted Answer

Step-by-step reasoning:

1. Number positions are top $p_1$ to bottom $p_7$. "Only three boxes between G and box number 9" gives possible pairs with distance 4. Considering "E is above 9" eliminates cases where 9 is at $p_1$ or $p_2$. The only feasible placement is $9$ at $p_3$, $B$ at $p_4$ and $G$ at $p_7$ (since B is below 9 and only two boxes between G and B).

2. "E is immediately below 12" and "E is above 9" force $12$ at $p_1$ and $E$ at $p_2$.

So far: $p_1=12,
 p_2=E,
 p_3=9,
 p_4=B,
 p_7=G$.

3. Remaining numbers are $\{2,4,5,7,8\}$ for $p_2,p_5,p_6,p_7,p_4$. E's number is not $7$ or $8$, so $E\in\{2,4,5\}$. The clue "There is only one box between E and the box having number less than E" with $E$ at $p_2$ means the smaller-numbered box must be at $p_4$ (one box between $p_2$ and $p_4$). Thus $B$ at $p_4$ has a number less than $E$.

4. "Only one box between B and box number 4" (with $B$ at $p_4$) places number $4$ at $p_6$ (because $p_2$ is occupied by $E$). So $p_6$ = number $4$.

5. Now try $E=5$ at $p_2$ (other small values lead to contradictions). Then $B$ at $p_4$ must be $2$ (the number less than $5$ at $p_4$). That leaves numbers $7$ and $8$ for $p_5$ and $p_7$; since $p_7$ is $G$, one of them is $G$.

6. "Only two boxes between number 5 and F" (number $5$ at $p_2$) forces $F$ at $p_5$.

7. "The difference between F and the box immediately below it is less than four." With $p_6=4$, $F$ at $p_5$ must be $7$ (difference $|7-4|=3<4$). So $p_5=7$ and $p_7=8$.

8. Place remaining letters: $p_3$ can be $C$ and $p_1$ the remaining box (consistently satisfying "C is not topmost" and "C's number is not 4"). Also "Only two boxes between C and A" is satisfied by $C$ at $p_3$ and $A$ at $p_6$.

Final layout (top to bottom):
$p_1$: 12 (D),
$p_2$: 5 (E),
$p_3$: 9 (C),
$p_4$: 2 (B),
$p_5$: 7 (F),
$p_6$: 4 (A),
$p_7$: 8 (G).

Thus the box immediately above $A$ (at $p_6$) is at $p_5$, which has number $7$. Therefore the correct option is Box number 7.

FINAL_ANSWER: c

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