Question 1
Seven positions (1 to 7, bottom to top) form a vertical stack. Only five boxes P, Q, R, S, and T are placed; the remaining two positions are empty.
Conditions:
- Box Q is at the top (position 7)
- Box P is at the bottom (position 1)
- Box R and Box S have exactly two entities (boxes or empty slots) between them
- One empty slot is at position 2
- Box T is immediately above the second empty slot
At which position is box T located?
Step-by-step Solution:
1. Fixed positions:
- Position 1 = P (bottom)
- Position 7 = Q (top)
- Position 2 = Empty (first empty slot - given)
2. Remaining positions to fill: 3, 4, 5, 6
- Need to place: R, S, T, and the second empty slot
3. Box T is immediately above the second empty slot:
- Let the second empty slot be at position X
- Then T must be at position X + 1
- Possible X values: 3, 4, 5 (since X+1 ≤ 7 and X+1 cannot be 7 because Q is there)
- X cannot be 6 because T would need to be at 7, but position 7 is Q
4. Try X = 3 (second empty at 3, T at 4):
- Remaining positions: 5 and 6 for R and S
- R and S at 5 and 6 → they are adjacent (0 entities between them)
- This violates "exactly two entities between R and S" ✗
5. Try X = 4 (second empty at 4, T at 5):
- Remaining positions: 3 and 6 for R and S
- Between positions 3 and 6: we have positions 4 and 5
- Position 4 = Empty, Position 5 = T
- That's exactly 2 entities between R and S ✓
- This works!
6. Try X = 5 (second empty at 5, T at 6):
- Remaining positions: 3 and 4 for R and S
- Between positions 3 and 4: no positions between them (0 entities)
- This violates the constraint ✗
7. Therefore, the only valid arrangement is X = 4:
- Position 3: R
- Position 4: Empty (second empty)
- Position 5: T
- Position 6: S
8. Final arrangement (bottom to top):
- Position 1: P
- Position 2: Empty
- Position 3: R
- Position 4: Empty
- Position 5: T
- Position 6: S
- Position 7: Q
9. Verification of all conditions:
- Q at top (7) ✓
- P at bottom (1) ✓
- R at 3, S at 6 → between them: positions 4 (Empty) and 5 (T) → exactly 2 entities ✓
- Empty slot at position 2 ✓
- T at position 5 is immediately above second empty at position 4 ✓
10. Answer: Box T is at position 5
Final Answer: Position 5
1. Fixed positions:
- Position 1 = P (bottom)
- Position 7 = Q (top)
- Position 2 = Empty (first empty slot - given)
2. Remaining positions to fill: 3, 4, 5, 6
- Need to place: R, S, T, and the second empty slot
3. Box T is immediately above the second empty slot:
- Let the second empty slot be at position X
- Then T must be at position X + 1
- Possible X values: 3, 4, 5 (since X+1 ≤ 7 and X+1 cannot be 7 because Q is there)
- X cannot be 6 because T would need to be at 7, but position 7 is Q
4. Try X = 3 (second empty at 3, T at 4):
- Remaining positions: 5 and 6 for R and S
- R and S at 5 and 6 → they are adjacent (0 entities between them)
- This violates "exactly two entities between R and S" ✗
5. Try X = 4 (second empty at 4, T at 5):
- Remaining positions: 3 and 6 for R and S
- Between positions 3 and 6: we have positions 4 and 5
- Position 4 = Empty, Position 5 = T
- That's exactly 2 entities between R and S ✓
- This works!
6. Try X = 5 (second empty at 5, T at 6):
- Remaining positions: 3 and 4 for R and S
- Between positions 3 and 4: no positions between them (0 entities)
- This violates the constraint ✗
7. Therefore, the only valid arrangement is X = 4:
- Position 3: R
- Position 4: Empty (second empty)
- Position 5: T
- Position 6: S
8. Final arrangement (bottom to top):
- Position 1: P
- Position 2: Empty
- Position 3: R
- Position 4: Empty
- Position 5: T
- Position 6: S
- Position 7: Q
9. Verification of all conditions:
- Q at top (7) ✓
- P at bottom (1) ✓
- R at 3, S at 6 → between them: positions 4 (Empty) and 5 (T) → exactly 2 entities ✓
- Empty slot at position 2 ✓
- T at position 5 is immediately above second empty at position 4 ✓
10. Answer: Box T is at position 5
Final Answer: Position 5