Question 1
Nine boxes A, B, C, D, E, F, G, H, and I are arranged in three vertical stacks (Stack X, Y, Z) with 3 boxes each. Positions are numbered 1-3 from bottom to top in each stack.
Conditions:
- Box A is in Stack X at position 2
- Box B is at the same position in Stack Y as box C in Stack Z
- Box C is at the top of Stack Z
- Box D is in Stack X at the bottom
- The sum of positions of box E in Stack Z and box F in Stack X equals 4
- Box G is immediately above box H in Stack Y
- Box I is in Stack Z at position 2
In which stack and position is box E located?
Step-by-step Solution:
1. Direct assignments from given conditions:
- Stack X, position 2 = A
- Stack X, position 1 = D (bottom)
- Stack Z, position 3 = C (top)
- Stack Z, position 2 = I
2. From condition 2: B is at same position in Y as C in Z
- C at position 3 in Z → B at position 3 in Y
3. From condition 6: G immediately above H in Stack Y
- They must occupy consecutive positions: (1,2) or (2,3)
- Position 3 is B, so G and H must be at positions 1 and 2
- H at 1 (bottom), G at 2 (immediately above)
4. Stack Y so far:
- Position 1: H
- Position 2: G
- Position 3: B
5. Remaining boxes: E and F for Stacks X and Z
- Stack X has position 3 available
- Stack Z has position 1 available
6. From condition 5: pos(E in Z) + pos(F in X) = 4
- E can only be at Z position 1 (since Z positions 2 and 3 are I and C)
- F can only be at X position 3 (since X positions 1 and 2 are D and A)
- Therefore: 1 + 3 = 4 ✓
7. Final arrangements:
- Stack X: D(1), A(2), F(3)
- Stack Y: H(1), G(2), B(3)
- Stack Z: E(1), I(2), C(3)
8. Answer: Box E is in Stack Z at position 1
Verification: All 7 conditions satisfied ✓
1. Direct assignments from given conditions:
- Stack X, position 2 = A
- Stack X, position 1 = D (bottom)
- Stack Z, position 3 = C (top)
- Stack Z, position 2 = I
2. From condition 2: B is at same position in Y as C in Z
- C at position 3 in Z → B at position 3 in Y
3. From condition 6: G immediately above H in Stack Y
- They must occupy consecutive positions: (1,2) or (2,3)
- Position 3 is B, so G and H must be at positions 1 and 2
- H at 1 (bottom), G at 2 (immediately above)
4. Stack Y so far:
- Position 1: H
- Position 2: G
- Position 3: B
5. Remaining boxes: E and F for Stacks X and Z
- Stack X has position 3 available
- Stack Z has position 1 available
6. From condition 5: pos(E in Z) + pos(F in X) = 4
- E can only be at Z position 1 (since Z positions 2 and 3 are I and C)
- F can only be at X position 3 (since X positions 1 and 2 are D and A)
- Therefore: 1 + 3 = 4 ✓
7. Final arrangements:
- Stack X: D(1), A(2), F(3)
- Stack Y: H(1), G(2), B(3)
- Stack Z: E(1), I(2), C(3)
8. Answer: Box E is in Stack Z at position 1
Verification: All 7 conditions satisfied ✓