Weight Comparison Stack
Weight Comparison Stack problems involve arranging boxes in a vertical stack where heavier boxes must be below lighter boxes, along with additional inequality constraints (e.g., 'Box A is heavier than Box B but lighter than Box C'). These puzzles test understanding of transitive inequalities and ordering.
What You'll Learn
Introduction to Weight Comparison Stack
Weight Comparison Stack problems involve arranging boxes in a vertical stack where heavier boxes must be below lighter boxes, along with additional inequality constraints (e.g., 'Box A is heavier than Box B but lighter than Box C'). These puzzles test understanding of transitive inequalities and ordering.
Prerequisites
How to Solve Weight Comparison Stack Problems
Step 1: List all boxes and given weight relationships (A > B means A heavier than B)
Step 2: Build a complete weight order using transitive properties
Step 3: Apply stacking rule: heaviest at bottom, lightest at top
Step 4: Map weight order to stack positions
Step 5: Answer questions about specific positions or removals
Step 6: Verify all constraints are satisfied
Example Problem
Example: Five boxes A-E stacked (positions 1-5 bottom to top). Heaviest at bottom. A > B but A < C. D is lightest. E > A but E < C. B > D. Which box is at position 3? Solution: Step 1: A > B and C > A → C > A > B Step 2: E > A and C > E → C > E > A Step 3: Combined: C > E > A > B Step 4: B > D → C > E > A > B > D Step 5: Weight order (heaviest to lightest): C, E, A, B, D Step 6: Stack (bottom to top): 1=C, 2=E, 3=A, 4=B, 5=D Step 7: Position 3 = A Answer: Box A
Pro Tips & Tricks
- Write inequalities as a chain: heaviest > ... > lightest
- Use transitivity: if A > B and B > C, then A > C
- If only some relationships are given, build partial order first
- Heaviest at bottom (position 1), lightest at top (position N)
- When boxes are removed, the remaining boxes shift while maintaining order
- Weight values may be given directly (e.g., 15kg, 25kg)
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Weight Comparison Stack. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Weight Comparison Stack is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Weight Comparison Stack?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: