Question 1
Six family members - Grandfather (G), Father (F), Uncle (U), Son (S), Nephew (N), and Grandson (GS) - have their boxes arranged in two vertical stacks (Stack A and Stack B), with 3 boxes in each stack. Positions are numbered 1 to 3 from bottom to top in each stack.
Family relationships (generations from oldest to youngest):
- Generation 1 (oldest): Grandfather (G)
- Generation 2: Father (F), Uncle (U)
- Generation 3: Son (S), Nephew (N)
- Generation 4 (youngest): Grandson (GS)
Conditions:
- No two boxes from the same generation are in the same stack
- The oldest generation member is at the bottom of Stack A
- Father's box is in Stack B
- Son's box is immediately above his son's (Grandson's) box
Which box is at the top of Stack A?
Step-by-step Solution:
1. Understand generations:
- Gen 1 (oldest): G
- Gen 2: F, U
- Gen 3: S, N
- Gen 4 (youngest): GS
2. Apply "oldest at bottom of Stack A":
- Stack A, position 1 = G
3. Apply "Father (F) in Stack B":
- F is in Stack B (position TBD)
4. Apply "Son (S) immediately above Grandson (GS)":
- They must be in same stack with S directly above GS
- Possible positions: (GS at 1, S at 2) or (GS at 2, S at 3)
- They cannot be in Stack A because G is at position 1
- So they must be in Stack B
- Place GS at position 1, S at position 2 in Stack B
5. Stack B so far:
- Position 1: GS (gen4)
- Position 2: S (gen3)
- Position 3: F (gen2) - must go here
6. Remaining boxes for Stack A:
- Used: G (Stack A), F, S, GS (Stack B)
- Remaining: U (gen2) and N (gen3)
7. Fill Stack A:
- Position 1: G (gen1)
- Position 2: N (gen3) - can't put U (gen2) adjacent to same gen? No same gen restriction applies to same stack
- Position 3: U (gen2)
8. Verify no same generation in same stack:
- Stack A: gen1 (G), gen3 (N), gen2 (U) → all different ✓
- Stack B: gen4 (GS), gen3 (S), gen2 (F) → all different ✓
9. Final arrangements:
- Stack A (bottom to top): G, N, U
- Stack B (bottom to top): GS, S, F
10. Answer: Box U (Uncle) is at the top of Stack A
Verification: All conditions satisfied ✓
1. Understand generations:
- Gen 1 (oldest): G
- Gen 2: F, U
- Gen 3: S, N
- Gen 4 (youngest): GS
2. Apply "oldest at bottom of Stack A":
- Stack A, position 1 = G
3. Apply "Father (F) in Stack B":
- F is in Stack B (position TBD)
4. Apply "Son (S) immediately above Grandson (GS)":
- They must be in same stack with S directly above GS
- Possible positions: (GS at 1, S at 2) or (GS at 2, S at 3)
- They cannot be in Stack A because G is at position 1
- So they must be in Stack B
- Place GS at position 1, S at position 2 in Stack B
5. Stack B so far:
- Position 1: GS (gen4)
- Position 2: S (gen3)
- Position 3: F (gen2) - must go here
6. Remaining boxes for Stack A:
- Used: G (Stack A), F, S, GS (Stack B)
- Remaining: U (gen2) and N (gen3)
7. Fill Stack A:
- Position 1: G (gen1)
- Position 2: N (gen3) - can't put U (gen2) adjacent to same gen? No same gen restriction applies to same stack
- Position 3: U (gen2)
8. Verify no same generation in same stack:
- Stack A: gen1 (G), gen3 (N), gen2 (U) → all different ✓
- Stack B: gen4 (GS), gen3 (S), gen2 (F) → all different ✓
9. Final arrangements:
- Stack A (bottom to top): G, N, U
- Stack B (bottom to top): GS, S, F
10. Answer: Box U (Uncle) is at the top of Stack A
Verification: All conditions satisfied ✓