Empty Position Stack
Empty Position Stack problems involve a vertical stack where some positions are empty (no box). You must arrange a smaller number of boxes in a larger number of positions, using constraints about which positions are empty and relationships between boxes.
What You'll Learn
Introduction to Empty Position Stack
Empty Position Stack problems involve a vertical stack where some positions are empty (no box). You must arrange a smaller number of boxes in a larger number of positions, using constraints about which positions are empty and relationships between boxes.
Prerequisites
How to Solve Empty Position Stack Problems
Step 1: Determine total positions (N) and number of boxes (M), with N > M
Step 2: Identify which positions are empty from given conditions
Step 3: Place all directly given boxes at their specified positions
Step 4: Apply constraints about box relationships (gaps, adjacency)
Step 5: Use elimination to place remaining boxes in non-empty positions
Step 6: Answer the specific question (position of a box or box at a position)
Example Problem
Example: Seven positions (1-7 bottom to top). Five boxes P-T placed; two positions empty. Q at top (7). P at bottom (1). One empty at position 2. R and S have exactly two entities between them. T immediately above second empty. Find T's position. Solution: Step 1: Position 1 = P, Position 7 = Q, Position 2 = Empty Step 2: Second empty at position X, T at X+1 Step 3: Try X=4 → T=5, positions 3,6 for R,S: between 3 and 6 = positions 4,5 (Empty,T) → 2 entities ✓ Step 4: T at position 5 Answer: Position 5
Pro Tips & Tricks
- Empty positions are 'entities' when counting boxes between
- Total positions = boxes + empty slots
- Empty slots have no box but occupy a position
- When counting 'entities between', count both boxes and empties
- The second empty is not necessarily the second empty in position order
- Use a placeholder (e.g., 'E') to mark empty positions
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Empty Position Stack. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Empty Position Stack is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Empty Position Stack?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: