Question 1

Five boxes labeled A, B, C, D, and E are stacked vertically on top of each other. The following conditions must be satisfied:
1. Box C is not at the top.
2. Box A is exactly 2 positions above Box D.
3. Box E is immediately above Box B.
4. Box D is not at the bottom.

Which box is at position 3 (middle position)?

Accepted Answer

Setup: We have 5 positions (1=bottom to 5=top). We need to place A, B, C, D, E using the four constraints.

Step 1: From constraint 3, E is immediately above B. This means B and E occupy consecutive positions. Possible pairs: (B,E) at (1,2), (2,3), (3,4), or (4,5).

Step 2: From constraint 2, A is exactly 2 positions above D. Possible pairs: (D,A) at (1,3), (2,4), or (3,5).

Step 3: From constraint 4, D is not at position 1 (bottom). So (D,A) must be at (2,4) or (3,5).

Step 4: From constraint 1, C is not at position 5 (top).

Step 5: Test (D,A) at (2,4):
- Positions: 2=D, 4=A
- Remaining positions: 1, 3, 5 for B, C, E
- From constraint 3, (B,E) must be consecutive. Options: (1,2)—no, 2 is taken. (3,4)—no, 4 is taken. (4,5)—no, 4 is taken.
- So (B,E) at (1,2) doesn't work. No valid arrangement here.

Step 6: Test (D,A) at (3,5):
- Positions: 3=D, 5=A
- Remaining positions: 1, 2, 4 for B, C, E
- From constraint 3, (B,E) consecutive: (1,2) or (4,5)—no, 5 is taken.
- So (B,E) at (1,2): Positions 1=B, 2=E, 3=D, 5=A, leaving 4=C.
- Check constraint 1: C at position 4 (not at top ✓)
- Check constraint 4: D at position 3 (not at bottom ✓)
- All constraints satisfied.

Final stack (bottom to top): B(1), E(2), D(3), C(4), A(5).
Position 3 = D.

Question 2

Five boxes labeled A, B, C, D, and E are stacked in a vertical arrangement (positions 1 to 5, where 1 is bottom and 5 is top). The following conditions must be satisfied:

1. Box C is exactly 2 positions above Box A.
2. Box B is immediately above Box D.
3. Box E is not at the top.
4. Box A is not at the bottom.
5. Box D is below Box A.

Which box is at position 3 (middle position)?

Accepted Answer

Setup: This is a constraint-satisfaction stacking puzzle requiring systematic elimination using relative position rules.

Solution:
From constraint 1: C is exactly 2 positions above A. Possible pairs: (A=1,C=3), (A=2,C=4), (A=3,C=5).
From constraint 4: A is not at position 1. So: (A=2,C=4) or (A=3,C=5).
From constraint 5: D is below A.

Case 1: A=2, C=4
- D must be at position 1 (below A=2).
- From constraint 2: B is immediately above D. So B=2. But A=2. Contradiction.

Case 2: A=3, C=5
- D must be at position 1 or 2 (below A=3).
- From constraint 2: B is immediately above D.
  - If D=1, then B=2. Remaining: E at position 4. Check constraint 3: E not at top. E=4 ✓. All constraints satisfied.
  - If D=2, then B=3. But A=3. Contradiction.

Final arrangement: D=1, B=2, A=3, E=4, C=5.
Position 3 contains Box A.

Trap explanation: Students often confuse "exactly 2 positions above" with "2 positions higher in numbering" and place C at position A+2 without checking other constraints, leading them to incorrectly select C. Others misread constraint 5 and place D above A, selecting D or E.

Question 3

Five boxes labeled A, B, C, D, and E are stacked vertically in positions 1 (bottom) to 5 (top). The following conditions must be satisfied:

1. Box C is exactly 2 positions above Box A.
2. Box B is immediately above Box D.
3. Box E is not at the top.
4. Box A is not at the bottom.
5. Box D is below Box C.

Which box is at position 3 (middle)?

Accepted Answer

Setup: We need to determine the unique vertical stacking order of 5 boxes given 5 constraints involving relative positions and adjacency.

Solution:
From constraint 1: C is exactly 2 positions above A. Possible pairs: (A at 1, C at 3), (A at 2, C at 4), or (A at 3, C at 5).

From constraint 4: A is not at position 1. This eliminates (A at 1, C at 3).
Remaining: (A at 2, C at 4) or (A at 3, C at 5).

From constraint 5: D is below C.

Case 1: A at 2, C at 4.
- D must be at position 1, 2, or 3 (below C at 4).
- D cannot be at 2 (A is there).
- From constraint 2: B is immediately above D.
- If D at 1, then B at 2 (but A is at 2). Contradiction.
- If D at 3, then B at 4 (but C is at 4). Contradiction.
- Case 1 fails.

Case 2: A at 3, C at 5.
- D must be at position 1, 2, 3, or 4 (below C at 5).
- D cannot be at 3 (A is there).
- From constraint 2: B is immediately above D.
- If D at 1, then B at 2. Remaining: E at 4. Check constraint 3: E not at top (position 5). E is at 4. ✓ All constraints satisfied.
  Stack: D(1), B(2), A(3), E(4), C(5).
- If D at 2, then B at 3 (but A is at 3). Contradiction.
- If D at 4, then B at 5 (but C is at 5). Contradiction.

Verification of solution D(1), B(2), A(3), E(4), C(5):
1. C at 5, A at 3: 5 - 3 = 2. ✓
2. B at 2, D at 1: B immediately above D. ✓
3. E at 4, not at position 5. ✓
4. A at 3, not at position 1. ✓
5. D at 1, C at 5: D below C. ✓

Position 3 contains Box A.

Trap Explanation: The most tempting wrong answer is E (position 4). Students often miscount the constraint "C is exactly 2 positions above A" and place them at positions 4 and 5 instead of 3 and 5, leading them to incorrectly deduce E at position 3. Another common error is placing B at position 3 by forgetting that constraint 2 requires B to be immediately adjacent to D, which forces them into positions 1–2 or 4–5, not position 3.

Shortcut: Start with the most restrictive constraint (constraint 2: B immediately above D). This creates a locked pair. Then use constraint 1 (C exactly 2 above A) to place the second pair. The locked pair B–D can only fit in positions (1,2), (2,3), (3,4), or (4,5). Test each: only (1,2) allows A at 3 and C at 5 without conflict. This eliminates 75% of possibilities in seconds.

RRB Group D Box / Stack Puzzle

Box / Stack Puzzle— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Box / Stack Puzzle — Practice Questions

60-Second Revision — Box / Stack Puzzle