3x3 Matrix Arrangement: Persons x Colors
3x3 Matrix Arrangement problems involve placing 9 persons (or objects) in a 3x3 grid, with each cell containing a unique person and a unique color. Constraints involve adjacency (orthogonal neighbors), opposite cells (diagonally opposite corners, opposite edges), and position properties (center, corners, edges).
What You'll Learn
Introduction to 3x3 Matrix Arrangement: Persons x Colors
3x3 Matrix Arrangement problems involve placing 9 persons (or objects) in a 3x3 grid, with each cell containing a unique person and a unique color. Constraints involve adjacency (orthogonal neighbors), opposite cells (diagonally opposite corners, opposite edges), and position properties (center, corners, edges).
Prerequisites
How to Solve 3x3 Matrix Arrangement: Persons x Colors Problems
Step 1: Draw a 3x3 grid with coordinates (row, col) where row and col range 1-3
Step 2: Identify special positions: corners (1,1),(1,3),(3,1),(3,3); edges (1,2),(2,1),(2,3),(3,2); center (2,2)
Step 3: Place directly given persons/colors at their positions
Step 4: Apply adjacency constraints (e.g., 'X is adjacent to Y')
Step 5: Apply opposite constraints (e.g., 'X sits opposite Y' in 2x2 subgrid)
Step 6: Use elimination to fill remaining cells
Step 7: Answer questions about positions or relationships
Example Problem
Example: 9 persons in 3x3 grid. Center cell is occupied by P who likes Red. Q sits opposite R on grid edges. S at a corner does not like Blue. T is adjacent to U. Find who occupies (row 3, col 2). Solution: Step 1: Draw 3x3 grid Step 2: Place P at (2,2) with Red Step 3: Opposite edges: (1,2) opposite (3,2), (2,1) opposite (2,3) Step 4: Apply corner and adjacency constraints Step 5: Eliminate to determine cell contents Answer: Person at (3,2) identified
Pro Tips & Tricks
- Corner cells: (1,1), (1,3), (3,1), (3,3)
- Edge cells (non-corner): (1,2), (2,1), (2,3), (3,2)
- Center cell: (2,2)
- Opposite corners: (1,1) opposite (3,3), (1,3) opposite (3,1)
- Opposite edges: (1,2) opposite (3,2), (2,1) opposite (2,3)
- Adjacent cells share a common side (up, down, left, right)
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master 3x3 Matrix Arrangement: Persons x Colors. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
3x3 Matrix Arrangement: Persons x Colors is an important topic for various competitive exams. Here's how frequently it appears:
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Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: