Multi-Stack Arrangement
Multi-Stack Arrangement problems involve two or more vertical stacks with relationships between boxes in different stacks (e.g., 'Box X in Stack A is at the same position as Box Y in Stack B'). These puzzles test your ability to coordinate multiple parallel arrangements.
What You'll Learn
Introduction to Multi-Stack Arrangement
Multi-Stack Arrangement problems involve two or more vertical stacks with relationships between boxes in different stacks (e.g., 'Box X in Stack A is at the same position as Box Y in Stack B'). These puzzles test your ability to coordinate multiple parallel arrangements.
Prerequisites
How to Solve Multi-Stack Arrangement Problems
Step 1: Identify all stacks and their position numbering (usually same for all)
Step 2: Create separate grids for each stack
Step 3: Place directly given boxes in their respective stacks
Step 4: Apply cross-stack constraints (e.g., same position, different positions)
Step 5: Use intra-stack constraints within each stack
Step 6: Solve simultaneously, updating all stacks as you deduce
Step 7: Answer the specific question
Example Problem
Example: Eight boxes A-H are in two stacks (Stack 1 and Stack 2), 4 boxes each (positions 1-4 bottom to top). Box A is at top of Stack 1. Box B is in Stack 2 at position 2. Box C is immediately below A in Stack 1. Box D is at same position in Stack 2 as C in Stack 1. Box E is at bottom of Stack 1. Box F is immediately above D in Stack 2. Which box is at bottom of Stack 2? Solution: Step 1: Stack 1 positions: 1(bottom)-4(top), Stack 2 same Step 2: Stack 1: pos4=A (top), pos1=E (bottom), C immediately below A → pos3=C Step 3: Stack 1 remaining: pos2 = G (remaining box) Step 4: D at same position as C in Stack 1 → Stack 2, pos3 = D Step 5: F immediately above D → Stack 2, pos4 = F Step 6: B at Stack 2, pos2 (given) Step 7: Stack 2 remaining: pos1 = H (remaining box) Answer: Box H is at bottom of Stack 2
Pro Tips & Tricks
- Draw each stack as a separate column
- 'Same position' means the position number is identical across stacks
- Cross-stack constraints link the two arrangements
- Each stack has its own set of boxes (no box appears in two stacks)
- Fill all positions in one stack before moving to the next when possible
- The total number of boxes = sum of stack capacities
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Multi-Stack Arrangement. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Multi-Stack Arrangement is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Multi-Stack Arrangement?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: