Single Stack Position Gap
Single Stack Position Gap problems involve arranging boxes in a vertical stack where constraints specify exact gaps between boxes (e.g., 'Box P is 3 positions above Box Q'). These puzzles require counting and arithmetic reasoning to determine exact positions.
What You'll Learn
Introduction to Single Stack Position Gap
Single Stack Position Gap problems involve arranging boxes in a vertical stack where constraints specify exact gaps between boxes (e.g., 'Box P is 3 positions above Box Q'). These puzzles require counting and arithmetic reasoning to determine exact positions.
Prerequisites
How to Solve Single Stack Position Gap Problems
Step 1: Understand the numbering system (bottom-to-top or top-to-bottom)
Step 2: Place all directly given boxes at their specified positions
Step 3: For gap constraints like 'X is k positions above Y', write: pos(X) = pos(Y) + k
Step 4: List all possible position pairs that satisfy each gap constraint
Step 5: Eliminate pairs that conflict with fixed positions
Step 6: Use process of elimination to determine the unique arrangement
Step 7: Answer the specific question
Example Problem
Example: Seven boxes P, Q, R, S, T, U, V are stacked vertically (positions 1-7, bottom to top). Box P is 3 positions above Box Q. Box R is immediately below Box S. Box T is at the bottom. Box U is between Box R and Box P. How many boxes are between Box S and Box V? Solution: Step 1: Fixed: Position 1 = T Step 2: P is 3 positions above Q: possible pairs (Q,P): (1,4), (2,5), (3,6), (4,7) Position 1 is T → (1,4) invalid Step 3: R immediately below S: consecutive positions with R below S: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7) Step 4: Try Q=2, P=5, S=3, R=2? Conflict (Q=2, R=2) → invalid Step 5: Try Q=3, P=6, S=4, R=3? Conflict → invalid Step 6: Try Q=4, P=7, S=3, R=2, then U between R(2) and P(7) → U at 5, V at 6 Step 7: S at 3, V at 6 → boxes between: positions 4,5 → 2 boxes Answer: 2 boxes
Pro Tips & Tricks
- 'k positions above' means pos(X) = pos(Y) + k
- 'k positions below' means pos(X) = pos(Y) - k
- 'Immediately above' means k = 1
- Count boxes between positions A and B as |pos(A) - pos(B)| - 1
- When multiple constraints exist, start with the most restrictive one
- Draw a blank stack and fill in possibilities gradually
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Single Stack Position Gap. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Single Stack Position Gap is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Single Stack Position Gap?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: