Floor/Box Puzzle
Floor/Box Puzzle problems involve arranging boxes on different floors of a building (or in a stack) with multiple attributes (color, city, item). Clues include specific floor assignments, gaps between boxes, adjacency, and even/odd floor constraints.
What You'll Learn
Introduction to Floor/Box Puzzle
Floor/Box Puzzle problems involve arranging boxes on different floors of a building (or in a stack) with multiple attributes (color, city, item). Clues include specific floor assignments, gaps between boxes, adjacency, and even/odd floor constraints.
Prerequisites
How to Solve Floor/Box Puzzle Problems
Step 1: Determine numbering system (1 = bottom or 1 = top)
Step 2: Create a table with floor numbers as rows
Step 3: Place directly assigned boxes at specified floors
Step 4: Apply gap constraints (e.g., 'exactly k boxes between')
Step 5: Apply adjacency constraints (e.g., 'immediately above/below')
Step 6: Use even/odd floor constraints to eliminate possibilities
Step 7: Answer questions about box positions or attributes
Example Problem
Example: Eight boxes on 8 floors (8 top to 1 bottom). Box A on top floor. Exactly 4 boxes between B and F. Box G immediately below F. Box C on odd floor not 1. Box H not on even floor. Find boxes between C and G. Solution: Step 1: Floors: 8(top) to 1(bottom) Step 2: A at floor 8 Step 3: 4 boxes between B and F → positions differ by 5 Step 4: G immediately below F → G at floor(F)-1 Step 5: C at odd floor (7,5,3,1) not 1 → 7,5,3 Step 6: H not on even floor → odd floor Step 7: Use elimination to determine positions Answer: Number of boxes between C and G
Pro Tips & Tricks
- Floors: N (top) to 1 (bottom) or 1 (bottom) to N (top) - read carefully
- 'Immediately above' means floor number +1 (if top=largest)
- 'Exactly k boxes between' means position difference = k+1
- Even floors: 2,4,6,...; Odd floors: 1,3,5,7,...
- Start with the most restrictive constraints
- Use a table to track possible floor assignments
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Floor/Box Puzzle. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Floor/Box Puzzle is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Floor/Box Puzzle?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: