Question 1
Eight positions (1 to 8, bottom to top) form a vertical stack. Only five boxes A, B, C, D, and E are placed; the remaining three positions are empty.
Conditions:
- Position 1 and position 8 are empty
- Box A is at position 5
- Box B is three positions below box C (i.e., position of C = position of B + 3)
- Box D is immediately above an empty position
- Box E is at an even-numbered position
Based on these conditions, at which position is box C located?
Step-by-step Solution:
1. Start with fixed information:
- Position 1 = Empty
- Position 8 = Empty
- Position 5 = A
2. List remaining positions for boxes B, C, D, E:
Available: 2, 3, 4, 6, 7
3. Apply "Box B is three positions below Box C":
- Possible (B, C) pairs: (2,5), (3,6), (4,7), (5,8)
- Position 5 is A, position 8 is Empty → (2,5) and (5,8) invalid
- Remaining: (3,6) or (4,7)
4. Apply "Box E is at an even position":
- Even positions available: 2, 4, 6
- Position 6 is a candidate for C in option (3,6) → then E would need another even
5. Apply "Box D is immediately above an empty position":
- Empty positions: 1 and 8 (fixed), plus possibly others
- Positions above empty:
* Above pos1 (empty) → position 2
* Above pos8 (empty) → none (pos9 doesn't exist)
- So D MUST be at position 2 (above empty pos1)
6. Place D at position 2
7. Re-evaluate B and C with D placed:
- Available now: 3, 4, 6, 7
- (B,C) options: (3,6) or (4,7)
8. Place E at even position:
- Even positions available: 4, 6 (2 is taken by D)
- Try (B,C) = (4,7):
* Then B=4, C=7
* E must be at even → E=6
* Remaining position 3 becomes Empty
- Check D at 2 (above empty pos1) ✓
- Check E at 6 (even) ✓
9. Final arrangement (bottom to top):
- Position 1: Empty
- Position 2: D
- Position 3: Empty
- Position 4: B
- Position 5: A
- Position 6: E
- Position 7: C
- Position 8: Empty
10. Answer: Box C is at position 7
Verification: All conditions satisfied ✓
1. Start with fixed information:
- Position 1 = Empty
- Position 8 = Empty
- Position 5 = A
2. List remaining positions for boxes B, C, D, E:
Available: 2, 3, 4, 6, 7
3. Apply "Box B is three positions below Box C":
- Possible (B, C) pairs: (2,5), (3,6), (4,7), (5,8)
- Position 5 is A, position 8 is Empty → (2,5) and (5,8) invalid
- Remaining: (3,6) or (4,7)
4. Apply "Box E is at an even position":
- Even positions available: 2, 4, 6
- Position 6 is a candidate for C in option (3,6) → then E would need another even
5. Apply "Box D is immediately above an empty position":
- Empty positions: 1 and 8 (fixed), plus possibly others
- Positions above empty:
* Above pos1 (empty) → position 2
* Above pos8 (empty) → none (pos9 doesn't exist)
- So D MUST be at position 2 (above empty pos1)
6. Place D at position 2
7. Re-evaluate B and C with D placed:
- Available now: 3, 4, 6, 7
- (B,C) options: (3,6) or (4,7)
8. Place E at even position:
- Even positions available: 4, 6 (2 is taken by D)
- Try (B,C) = (4,7):
* Then B=4, C=7
* E must be at even → E=6
* Remaining position 3 becomes Empty
- Check D at 2 (above empty pos1) ✓
- Check E at 6 (even) ✓
9. Final arrangement (bottom to top):
- Position 1: Empty
- Position 2: D
- Position 3: Empty
- Position 4: B
- Position 5: A
- Position 6: E
- Position 7: C
- Position 8: Empty
10. Answer: Box C is at position 7
Verification: All conditions satisfied ✓