Seating Arrangements: Systematic Approach

Types of Arrangements

Linear (Row)

• Single row: Left to right
• Double row: Facing each other or same direction
• Direction matters: Left/Right

Circular

• All facing center
• All facing outside
• Alternating directions
• Key: No absolute left/right, only relative positions

Rectangular/Square

• 4 sides, people on each side
• Corner positions vs Middle positions

Solution Strategy

Step 1: List All Clues

• Definite: "A sits at position 3"
• Relative: "B is left of C"
• Conditional: "If A sits here, then B sits there"

Step 2: Start with Most Restrictive

• Fixed positions
• Unique conditions
• Endpoints in linear arrangements

Step 3: Use Grid/Diagram

• Draw the arrangement
• Mark positions as you deduce
• Use pencil for tentative placements

Step 4: Check Consistency

• Verify all clues satisfied
• Look for contradictions
• Eliminate impossible cases

Common Patterns

Immediate Neighbors

• "A and B sit together" → Adjacent positions

Not Together

• "A and B don't sit together" → At least one person between

Between

• "C sits between A and B" → A-C-B or B-C-A

Facing

• In double row: Directly opposite

Circular Arrangement Tips

• Fix one person's position (to avoid rotational duplicates)
• Count clockwise or anticlockwise consistently
• Opposite position = n/2 positions away (if n people)

CAT Strategy

• Time limit: 15-20 minutes for complex set
• If stuck after 5 minutes, move to next set
• Draw clear diagrams
• Use symbols for quick notation
• Practice 2-3 sets daily