Box/Stack Puzzles Worksheet 23 - Advanced Level (stack puzzles) | 20 Questions

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 ✓

three-stacks, inter-stack, mathematical

Question 2

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 ✓

family-relations, generation, real-world

Question 3

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

vertical, gaps, empty_slots, banking_clerk

Question 4

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

vertical, gaps, empty_slots, banking_clerk

Question 5

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 ✓

three-stacks, inter-stack, mathematical

Question 6

Six boxes A, B, C, D, E, and F are arranged in a rack with 2 rows and 3 columns. Row 1 (top): Positions 1, 2, 3 (left to right) Row 2 (bottom): Positions 4, 5, 6 (left to right) Conditions: - Box A is in Row 1 - Box B is directly below box C - Box D is at position 4 (bottom-left) - Box E is to the immediate right of box A - Box F is in Row 2 but not below box A Which box is at position 5?

Step-by-step Solution:

1. Understand the layout:
- Row 1 (top): positions 1 (Col1), 2 (Col2), 3 (Col3)
- Row 2 (bottom): positions 4 (Col1), 5 (Col2), 6 (Col3)
- "Directly below" means same column, consecutive rows
- "Immediate right" means same row, adjacent columns

2. Direct assignment:
- Position 4 = D (given)

3. Place A and E:
- A in Row 1 (positions 1, 2, or 3)
- E immediately right of A
- Possible pairs: (A=1, E=2) or (A=2, E=3)
- Try A=1, E=2 first

4. Place B and C (B directly below C):
- Possible column pairs: (C at pos1, B at pos4), (C at pos2, B at pos5), (C at pos3, B at pos6)
- pos4 is already D, so (C=1, B=4) invalid
- Try C=3, B=6 (Column 3)

5. Place remaining box F:
- Available position: pos5
- F in Row 2 (pos5) and not below A
- A at pos1 (Col1), F at pos5 (Col2) → not below ✓

6. Final arrangement:
- Position 1: A
- Position 2: E
- Position 3: C
- Position 4: D
- Position 5: F
- Position 6: B

7. Answer: Box F is at position 5

Verification: All conditions satisfied ✓

rows-columns, grid-arrangement, spatial

Question 7

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 ✓

three-stacks, inter-stack, mathematical

Question 8

Five boxes P, Q, R, S, and T are in a stack numbered 1 to 5 from TOP to BOTTOM (1 is topmost, 5 is bottommost). Given conditions: - Box P is at the top (position 1) - Box Q is at the bottom (position 5) - Box S is immediately above box T - Box R is at position 4 Which box is at position 4 from the top?

Step-by-step Solution:

1. Understanding the numbering system:
- Position 1 = TOP
- Position 5 = BOTTOM

2. Fixed positions:
- Position 1 = P
- Position 5 = Q
- Position 4 = R

3. Remaining positions: 2 and 3 for boxes S and T

4. "S is immediately above T":
- They must occupy consecutive positions with S above T
- Therefore: S at position 2, T at position 3

5. Final arrangement (top to bottom):
- Position 1: P
- Position 2: S
- Position 3: T
- Position 4: R
- Position 5: Q

6. Answer: Box R is at position 4

Verification: All conditions satisfied ✓

numbering-system, top-to-bottom, basic

Question 9

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

vertical, gaps, empty_slots, banking_clerk

Question 10

Seven boxes A, B, C, D, E, F, and G are stacked vertically (positions 1 to 7 from bottom to top). Given conditions: - Box C is at position 3 - The product of the positions of boxes C and D is 12 - Box E is at a prime-numbered position - Box F is at a position that is 5 more than twice the position of box G - The sum of the positions of boxes A and B is 8, with box A below box B - Box D is at an even-numbered position - Box G is at an odd-numbered position What is the position of box A?

Step-by-step Solution:

1. Start with fixed information:
- Position 3 = C (given)

2. Product condition: pos(C) × pos(D) = 12
- 3 × pos(D) = 12
- pos(D) = 4

3. Box D is at even position: 4 is even ✓

4. Prime position for Box E: Prime positions are 2, 3, 5, 7
- Position 3 is C, so E can be at 2, 5, or 7

5. F and G relationship: pos(F) = 5 + 2 × pos(G)
- Possible (G, F) pairs: (1,7), (2,9-invalid), (3,11-invalid)
- Therefore: G at 1, F at 7

6. Sum condition: pos(A) + pos(B) = 8, with pos(A) < pos(B) (A below B)
- Possible pairs: (1,7), (2,6), (3,5)
- Position 1 is G, position 3 is C, position 7 is F
- Therefore: (1,7) and (3,5) invalid
- Only possibility: A at 2, B at 6

7. Box E must be at prime position:
- Remaining position after placing A(2), B(6), C(3), D(4), F(7), G(1)
- Only position left is 5 for E
- 5 is prime ✓

8. Final arrangement (bottom to top):
- Position 1: G
- Position 2: A
- Position 3: C
- Position 4: D
- Position 5: E
- Position 6: B
- Position 7: F

9. Answer: Box A is at position 2

Verification of all conditions:
- C at position 3 ✓
- C(3) × D(4) = 12 ✓
- E at position 5 (prime) ✓
- F(7) = 5 + 2×G(1) ✓
- A(2) + B(6) = 8, A below B (2 < 6) ✓
- D at even position (4) ✓
- G at odd position (1) ✓

Answer: Position 2

mathematical, arithmetic, prime-numbers

Question 11

Six boxes A, B, C, D, E, and F are arranged in a rack with 2 rows and 3 columns. Row 1 (top): Positions 1, 2, 3 (left to right) Row 2 (bottom): Positions 4, 5, 6 (left to right) Conditions: - Box A is in Row 1 - Box B is directly below box C - Box D is at position 4 (bottom-left) - Box E is to the immediate right of box A - Box F is in Row 2 but not below box A Which box is at position 5?

Step-by-step Solution:

1. Understand the layout:
- Row 1 (top): positions 1 (Col1), 2 (Col2), 3 (Col3)
- Row 2 (bottom): positions 4 (Col1), 5 (Col2), 6 (Col3)
- "Directly below" means same column, consecutive rows
- "Immediate right" means same row, adjacent columns

2. Direct assignment:
- Position 4 = D (given)

3. Place A and E:
- A in Row 1 (positions 1, 2, or 3)
- E immediately right of A
- Possible pairs: (A=1, E=2) or (A=2, E=3)
- Try A=1, E=2 first

4. Place B and C (B directly below C):
- Possible column pairs: (C at pos1, B at pos4), (C at pos2, B at pos5), (C at pos3, B at pos6)
- pos4 is already D, so (C=1, B=4) invalid
- Try C=3, B=6 (Column 3)

5. Place remaining box F:
- Available position: pos5
- F in Row 2 (pos5) and not below A
- A at pos1 (Col1), F at pos5 (Col2) → not below ✓

6. Final arrangement:
- Position 1: A
- Position 2: E
- Position 3: C
- Position 4: D
- Position 5: F
- Position 6: B

7. Answer: Box F is at position 5

Verification: All conditions satisfied ✓

rows-columns, grid-arrangement, spatial

Question 12

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

vertical, gaps, empty_slots, banking_clerk

Question 13

Six boxes A, B, C, D, E, F are stacked vertically (positions 1-6, bottom to top). Each box has a different color: Red, Blue, Green, Yellow, White, and Pink. Given conditions: - Box A is Red and at position 4 - The Blue box is immediately above the Green box - Box B is Yellow and at the bottom (position 1) - Box C is at position 5 - The White box is at position 5 - The Pink box is at the top (position 6) - Box D is Blue What is the color of box C?

Step-by-step Solution:

1. Direct assignments from conditions:
- Position 1 = Box B (Yellow) [bottom]
- Position 4 = Box A (Red)
- Position 5 = Box C (also White box)
- Position 6 = Pink box

2. Blue immediately above Green:
- Possible consecutive pairs: (1,2), (2,3), (3,4), (4,5), (5,6)
- Position 4 is Red, position 5 is White, position 6 is Pink
- Position 1 is Yellow (B)
- Therefore, Green and Blue must be at positions 2 and 3
- Green at 2, Blue at 3 (Blue above Green) ✓

3. Box D is Blue:
- Blue at position 3 → Box D at position 3

4. Remaining box E:
- All positions filled: 1(B), 2(E/Green), 3(D/Blue), 4(A/Red), 5(C/White), 6(F/Pink)
- Therefore, box E must be at position 2 (Green)

5. Final stack (bottom to top):
- Position 1: B (Yellow)
- Position 2: E (Green)
- Position 3: D (Blue)
- Position 4: A (Red)
- Position 5: C (White)
- Position 6: F (Pink)

6. Answer: Box C is White

Verification of all conditions:
- A at position 4, Red ✓
- Blue (pos3) immediately above Green (pos2) ✓
- B at bottom, Yellow ✓
- C at position 5 ✓
- White box at position 5 ✓
- Pink at top ✓
- D is Blue ✓
- All colors unique ✓
- All positions filled ✓

color-coding, multi-parameter, vertical-stack

Question 14

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?

Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

temporal, operations, dynamic-stacking

Question 15

Seven boxes A, B, C, D, E, F, and G are stacked vertically (positions 1 to 7 from bottom to top). Given conditions: - Box C is at position 3 - The product of the positions of boxes C and D is 12 - Box E is at a prime-numbered position - Box F is at a position that is 5 more than twice the position of box G - The sum of the positions of boxes A and B is 8, with box A below box B - Box D is at an even-numbered position - Box G is at an odd-numbered position What is the position of box A?

Step-by-step Solution:

1. Start with fixed information:
- Position 3 = C (given)

2. Product condition: pos(C) × pos(D) = 12
- 3 × pos(D) = 12
- pos(D) = 4

3. Box D is at even position: 4 is even ✓

4. Prime position for Box E: Prime positions are 2, 3, 5, 7
- Position 3 is C, so E can be at 2, 5, or 7

5. F and G relationship: pos(F) = 5 + 2 × pos(G)
- Possible (G, F) pairs: (1,7), (2,9-invalid), (3,11-invalid)
- Therefore: G at 1, F at 7

6. Sum condition: pos(A) + pos(B) = 8, with pos(A) < pos(B) (A below B)
- Possible pairs: (1,7), (2,6), (3,5)
- Position 1 is G, position 3 is C, position 7 is F
- Therefore: (1,7) and (3,5) invalid
- Only possibility: A at 2, B at 6

7. Box E must be at prime position:
- Remaining position after placing A(2), B(6), C(3), D(4), F(7), G(1)
- Only position left is 5 for E
- 5 is prime ✓

8. Final arrangement (bottom to top):
- Position 1: G
- Position 2: A
- Position 3: C
- Position 4: D
- Position 5: E
- Position 6: B
- Position 7: F

9. Answer: Box A is at position 2

Verification of all conditions:
- C at position 3 ✓
- C(3) × D(4) = 12 ✓
- E at position 5 (prime) ✓
- F(7) = 5 + 2×G(1) ✓
- A(2) + B(6) = 8, A below B (2 < 6) ✓
- D at even position (4) ✓
- G at odd position (1) ✓

Answer: Position 2

mathematical, arithmetic, prime-numbers

Question 16

Five boxes A, B, C, D, and E are stacked vertically (positions 1-5, bottom to top). Their weights follow certain rules: - The heaviest box is at the bottom - Box A is heavier than box B but lighter than box C - Box D is the lightest - Box E is heavier than A but lighter than C - Box B is heavier than D Which box is at position 3?

Step-by-step Solution:

1. Establish weight relationships:
- A > B and C > A → So C > A > B
- D is lightest → D is smallest
- E > A and C > E → So C > E > A
- B > D

2. Combine all inequalities:
- From C > E > A and A > B, we get: C > E > A > B
- And B > D, so: C > E > A > B > D

3. Complete weight order (heaviest to lightest):
C > E > A > B > D

4. Stacking rule: Heaviest at bottom (position 1), lightest at top (position 5)
- Position 1 (bottom): C (heaviest)
- Position 2: E
- Position 3: A
- Position 4: B
- Position 5 (top): D (lightest)

5. Answer: Box A is at position 3

Verification:
- Heaviest (C) at bottom ✓
- A heavier than B (pos3 vs pos4) ✓
- A lighter than C (pos3 vs pos1) ✓
- D lightest at top ✓
- E heavier than A (pos2 vs pos3) ✓
- E lighter than C (pos2 vs pos1) ✓
- B heavier than D (pos4 vs pos5) ✓

weight-comparison, ordering, vertical-stack

Question 17

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?

Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

temporal, operations, dynamic-stacking

Question 18

Five boxes P, Q, R, S, and T are in a stack numbered 1 to 5 from TOP to BOTTOM (1 is topmost, 5 is bottommost). Given conditions: - Box P is at the top (position 1) - Box Q is at the bottom (position 5) - Box S is immediately above box T - Box R is at position 4 Which box is at position 4 from the top?

Step-by-step Solution:

1. Understanding the numbering system:
- Position 1 = TOP
- Position 5 = BOTTOM

2. Fixed positions:
- Position 1 = P
- Position 5 = Q
- Position 4 = R

3. Remaining positions: 2 and 3 for boxes S and T

4. "S is immediately above T":
- They must occupy consecutive positions with S above T
- Therefore: S at position 2, T at position 3

5. Final arrangement (top to bottom):
- Position 1: P
- Position 2: S
- Position 3: T
- Position 4: R
- Position 5: Q

6. Answer: Box R is at position 4

Verification: All conditions satisfied ✓

numbering-system, top-to-bottom, basic

Question 19

Five boxes A, B, C, D, and E are stacked one above another (bottom to top numbered 1 to 5). Box C is at position 3. Box A is immediately above box B. Box D is at the bottom. Which box is at the top of the stack?

Step-by-step Solution:

1. Create position table (1 = bottom, 5 = top)

2. Direct assignments:
- Box D is at bottom → Position 1 = D
- Box C is at position 3 → Position 3 = C

3. Key constraint: Box A is immediately above Box B
- They must occupy consecutive positions: (1,2), (2,3), (3,4), or (4,5)
- Position 1 is D, Position 3 is C → only (4,5) is available
- Therefore: Position 4 = B, Position 5 = A

4. Remaining box: E goes to Position 2

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

6. Answer: Box A is at the top

Verification: All constraints satisfied ✓

vertical-stack, immediate-neighbor, basic

Question 20

Six boxes P, Q, R, S, T, and U are in a vertical stack (positions 1-6, bottom to top). Given conditions: - If P is above Q, then R is at an even position - S is exactly in the middle of the stack - U is not adjacent to S - T is at the bottom - P is two positions above Q Based on these conditions, which box can NEVER be at the top (position 6)?

Step-by-step Solution:

1. Fixed positions from given conditions:
- T is at bottom → Position 1 = T
- S is exactly in the middle → For 6 boxes, middle positions are 3 or 4
- P is two positions above Q → P's position = Q's position + 2

2. Determine valid arrangement:
- Since P = Q + 2, possible pairs: (1,3), (2,4), (3,5), (4,6)
- Position 1 is T, so (1,3) invalid
- Try Q=2, P=4:
* Then S can be at position 3 (middle)
* R must be at even position (2,4,6) but 2 and 4 taken → R=6
* U must not be adjacent to S (pos3) → cannot be at 2 or 4 → U=5
* All positions filled: 1=T, 2=Q, 3=S, 4=P, 5=U, 6=R ✓

3. Test if each box can be at top (position 6):
- T: Fixed at bottom → Cannot be at top ❌
- Q: If Q at 6, then P would be at 8 (invalid) → Cannot be at top ❌
- P: Can be at top if Q=4, P=6 (with S=3, R=2, U=5) → Possible ✓
- R: Can be at top as shown in our arrangement → Possible ✓
- S: Can be at top if S=6 (but then middle would be 3, possible with adjustments) → Possible ✓
- U: Can be at top with different arrangement → Possible ✓

4. Only Q and T cannot be at top:
- T is explicitly fixed at bottom
- Q is mathematically impossible at top due to P=Q+2 constraint

5. The question asks "which box" (singular):
- Since T is explicitly stated to be at bottom, it's obvious
- Q is the non-obvious answer that requires deduction
- Therefore, Q is the intended answer

Answer: Box Q can never be at the top

Verification:
- In any valid arrangement, Q's maximum position is 4 (when P=6)
- Q at position 6 would require P at 8 (outside stack)
- Therefore Q is impossible at top ✓

conditional, either-or, complex-logic

Box/Stack Puzzles - Advanced Level: stack puzzles ADVANCED

What you'll learn in this worksheet:

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20