Linear Arrangements
Linear Arrangements
Linear arrangement problems involve seating people in a straight row, often with conditions about relative positions, facing directions, and gaps between people.
Key Idea
Fix one person's position first (preferably the most constrained one), then place others relative to that anchor. Track facing direction separately from left-right position.
Core Rules
Anchor Strategy
Start with the person who has the most conditions or a fixed position
Always — reduces the number of possibilities to test.
Facing Direction
If all face north: left = west side, right = east side. If someone faces south, their left/right reverses.
When the problem specifies facing directions (common in banking exams).
Gap Condition
"Exactly N people between A and B" means |Position_A - Position_B| = N + 1
When conditions specify people sitting between two individuals.
Immediate Neighbor
"A sits immediately to the left of B" means Position_A = Position_B - 1 (when facing the same direction)
When adjacency conditions are given.
Elimination by Contradiction
If placing a person in a position violates any condition, eliminate that case entirely
When multiple valid placements exist — test each and discard contradictions.
Relevant Exams
Linear arrangements appear as a 5-question set in IBPS PO and SBI PO prelims. Mastering the anchor-and-eliminate method is essential for solving within 5-7 minutes per set.