What is the position of D in the given stack of boxes?

Question

Accepted Answer

Step-by-step solution:

1. Let positions be $1$ (top) to $7$ (bottom). From "Only three boxes are kept between G and box number 9" the possible pairs (pos difference $4$) restrict 9 to positions $3,5,6,7$ because E must be above 9 and 12 must be above E (so 9 cannot be $1$ or $2$).

2. Try $9$ at position $3$. Then $G$ must be at position $7$ (three boxes between). "Only two boxes are kept between G and B" makes $B$ at position $4$ (since $G$ is at $7$).

3. "B is kept below box number 9" is satisfied ($B$ at $4$, $9$ at $3$). "Only one box is kept between B and box number 4" forces number $4$ to be at position $6$ (position $2$ is not possible because of E/12 requirement below).

4. E must be immediately below 12 and above 9. The only consecutive places above position $3$ are positions $1$ and $2$, so position $1$ = 12 and position $2$ = E. Thus E is at $2$, 12 at $1$, and 9 at $3$.

5. "There is only one box between E and the box having number less than E" => that smaller-number box must be at position $4$ (one box between positions $2$ and $4$). Position $4$ is $B$, so $B$'s number $<$ E's number.

6. E's number is neither $7$ nor $8$, so E must be $5$ (the only choice that allows a smaller number for $B$). Hence $E=5$ (pos $2$) and $B=2$ (pos $4$). Remaining numbers are $7$ and $8$ for positions $5$ and $7$.

7. "Only two boxes are kept between box number 5 and F" (positions differ by $3$) places $F$ at position $5$ (since 5 is at position $2$). The number left for $F$ must satisfy "difference between F and the box immediately below it is less than four": the box below position $5$ is position $6$ with number $4$, so $F$ must be $7$ (|7-4|=3<4), not $8$. Thus $F=7$ (pos $5$) and $G=8$ (pos $7$).

8. Remaining labels A and C must have exactly two boxes between them (positions differ by $3$). The only available pair is positions $3$ and $6$. C cannot be topmost and C's number is not $4$, so C must be at position $3$ and A at position $6$ (A's number = 4). The only remaining label for position $1$ is D with number $12$.

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

Therefore D is first from the top.

FINAL_ANSWER: c

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