What is the number of box C?

Question

Accepted Answer

Step-by-step solution:

1. Let the seven vertical positions be numbered from top to bottom as $1$ to $7$.

2. From the clues: “E is immediately below box number $12$” and “E is above box number $9$”, the only way to place these three numbers with $12$ immediately above $E$ and $E$ somewhere above $9$ is to put $12$ at position $1$, $E$ at position $2$ and $9$ at position $3$.

3. The clue “Only three boxes are kept between G and box number $9$” forces $G$ to be at position $7$ (since $9$ is at $3$ and positions differ by $4$). So $G$ is at $7$.

4. “Only two boxes are kept between G and B” and “B is below box number $9$” together force $B$ to be at position $4$ (three positions away from $G$ and below $9$). Thus $B$ occupies position $4$.

5. "Only one box is kept between B and box number $4$" then places the number $4$ at position $6$ (because $B$ is at $4$, so $4$ must be either at $2$ or $6$, but position $2$ is already $E$).

6. From "E's box number is neither $7$ nor $8$" and "There is only one box between E and the box having number less than E", $E$ must be $5$ at position $2$ (the only workable choice), which makes the box with a number less than $5$ occupy position $4$; that forces $B$'s number to be $2$ at position $4$.

7. "Only two boxes are kept between box number $5$ and F" places $F$ at position $5$ (since $5$ is at position $2$ and they must be three positions apart).

8. "The difference between F and the box immediately below it is less than four" with the box immediately below $F$ at position $6$ being $4$ forces $F$ to be $7$ (difference $|7-4|=3<4$). So position $5$ is $7$ and position $7$ (which is $G$) must be $8$ (the only remaining number).

9. The remaining numbers and boxes to place are $12$ (pos $1$), $9$ (pos $3$), $4$ (pos $6$) and the remaining box labels $A,C,D$ for positions $1,3,6$. The clue "C is not the topmost box" and "C's box number is not $4$" exclude position $1$ and position $6$ for $C$, so $C$ must be at position $1$ — the only remaining valid position.

10. Therefore box $C$ is at position $1$ and carries the number $12$.

FINAL_ANSWER: c

Answer

Answer

Answer

Answer