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Single Stack Position Gap: Worksheet 2 - Beginner Practice Single Stack Position Gap BEGINNER

Ready to master Single Stack Position Gap? This entry level practice worksheet (2/10) presents 20 beginner-level challenges. Focus area: pattern recognition. Learn to solve single stack position gap reasoning questions, handle single stack position gap practice, and perfect single stack position gap for competitive exams with our step-by-step solutions.

📝 Worksheet 2 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner level

What you'll learn in this worksheet:
Your progress through Single Stack Position Gap
Worksheet 2 of 10 (11% complete)

Question 1

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 2

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 3

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 4

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 5

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 6

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 7

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 8

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 9

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 10

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 11

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 12

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 13

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 14

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 15

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 16

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 17

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 18

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 19

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓

Question 20

Seven boxes P, Q, R, S, T, U, and V are arranged in a vertical stack (positions 1 to 7 from bottom to top). Box P is three positions above box Q. Box R is immediately below box S. Box T is at the bottom. Box U is somewhere between box R and box P. How many boxes are there between box S and box V?
Step-by-step Solution:

1. Create vertical stack (1=bottom, 7=top)

2. Direct assignments:
- Box T at bottom → Position 1 = T

3. Constraint 1: Box P is 3 positions above Box Q
- Possible pairs: (1,4), (2,5), (3,6), (4,7)
- Position 1 is T, so (1,4) invalid
- Try Q at 4, P at 7

4. Constraint 2: Box R immediately below Box S
- They occupy consecutive positions: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7)
- Position 4 is Q, position 7 is P
- Try R at 2, S at 3

5. Constraint 3: Box U between R and P
- R at 2, P at 7 → positions between: 3,4,5,6
- Position 3 is S, position 4 is Q
- Place U at position 5
- Remaining box V goes to position 6

6. Final arrangement (bottom to top):
- Position 1: T
- Position 2: R
- Position 3: S
- Position 4: Q
- Position 5: U
- Position 6: V
- Position 7: P

7. Count boxes between S (pos3) and V (pos6):
- Positions between: 4 and 5 → Boxes Q and U
- Total: 2 boxes

Answer: 2 boxes

Verification:
- T at bottom ✓
- P at 7, Q at 4 → 3 positions above ✓
- R at 2, S at 3 → immediately below ✓
- U at 5 is between R(2) and P(7) ✓
- All boxes used exactly once ✓
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