Which of the following boxes is numbered 8?

Question

Accepted Answer

Step-by-step reasoning:

1. Number the vertical positions from top = 1 to bottom = 7. From “Only three boxes are between G and box 9” the possible position pairs are 3 apart (distance 4). Considering all constraints, the only viable placements are p(G)=7 and p(9)=3 (so there are positions 4,5,6 between them).

2. “Only two boxes are between G and B” ⇒ p(B) must be 4 (since G is at 7 and there must be exactly two boxes between them: positions 5 and 6). Also B is below box 9 (p(B)>p(9)), which is satisfied by p(B)=4 and p(9)=3.

3. “E is immediately below 12” and “E is above box 9 (p=3)” imply p(E)=2 and p(12)=1.

4. E’s number is not 7 or 8 and “There is only one box between E and the box having number less than E.” If E were 2 this is impossible, so E must be 5 (the only viable choice that allows exactly one box between E (pos 2) and the box with a smaller number at pos 4). Thus p(2)=4 must be at pos 4 or pos 4 must be the smaller number; this leads to p(B)=4 being number 2.

5. From p(E)=2 (number 5) and “Only two boxes are between box number 5 and F,” we get p(F)=5 (since positions 2 and 5 differ by 3 positions, i.e. two boxes between).

6. “Only one box is between B and box number 4” with p(B)=4 forces box number 4 to be at pos 6 (one box, pos5, between pos4 and pos6).

7. Remaining numbers are now {7,8} for positions 5 and 7. The constraint “difference between F and the box immediately below it is less than 4” requires that if F is at pos5 then the number at pos6 must differ from F by <4. Putting 7 at pos5 and 4 at pos6 gives |7−4|=3<4, so p5=7 and p6=4. The remaining number 8 goes to pos7 (G).

8. Place remaining boxes A, C, D into positions 1,3,6. "C is not topmost" and "C's number is not 4" force C to be at pos3 (number 9), A at pos6 (number 4) and D at pos1 (number 12). Also "Only two boxes between C and A" holds (positions 3 and 6 have two boxes between).

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

Thus the box numbered 8 is G, i.e. option (4).

FINAL_ANSWER: d

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