Seating Arrangement
Overview
These problems test your ability to organize information systematically and draw logical conclusions from given conditions.
The topic divides into two main types: Linear Arrangement (persons sitting in a row) and Circular Arrangement (persons sitting around a table). SBI Clerk Prelims focuses on single-variable arrangements with moderate complexity—usually 5-8 persons with direct clues. Mastering this topic is non-negotiable; it's a reliable scoring area once you develop a systematic approach.
Success here depends on three skills: accurate diagram-making, careful clue interpretation, and methodical elimination. Students who rush through clues or draw messy diagrams lose marks to silly errors, not lack of understanding.
Key Concepts
- Linear Arrangement: Persons sit in a single row. Critical question: Are they facing North or South? If not mentioned, assume facing North (left = West, right = East).
- Circular Arrangement: Persons sit around a round table. Key detail: Are they facing the center or facing outside? This reverses the meaning of "left" and "right."
- Definite vs. Conditional Clues: Start with definite clues (exact positions like "A sits at the left end") before processing conditional clues ("B sits to the left of C" without exact position).
- Immediate vs. Non-Immediate Neighbors: "A sits next to B" means they are adjacent. "A sits to the left of B" may or may not mean adjacent—check for words like "immediately."
- Multiple Possibilities: Sometimes clues allow 2-3 valid configurations. Mark both cases and eliminate using later clues.
- Direction Convention: In circular facing center—a person's left is your right when you look at them. In circular facing outside—a person's left is also your left.
- Counting Positions: In linear rows, count positions from Left End or Right End as specified. Position 1 from left end = leftmost seat.
Key Facts to Remember
| Scenario | Left-Right Rule |
|---|---|
| Linear facing North | Left = West, Right = East |
| Linear facing South | Left = East, Right = West |
| Circular facing center | Clockwise = Right of the person |
| Circular facing outside | Clockwise = Left of the person |
Must-Remember Points:
- "Opposite" in circular = directly across the table (for 8 persons, 3 persons between them on either side)
- "Second to the left" = skip one person, count two positions leftward
- In a row of n persons, person at position k from left is at position (n-k+1) from right
- "Neither A nor B sits at the end" = both are somewhere in the middle
- "A and B are not neighbors" = at least one person sits between them
Worked Examples
Example 1: Linear Arrangement
Problem: Five persons P, Q, R, S, T sit in a row facing North.
- R sits at the right end.
- Q sits second to the left of R.
- P is an immediate neighbor of Q.
- S does not sit at any end.
Find: Who sits at the left end?
Solution:
- Step 1: Draw 5 positions. R at right end → Position 5.
- Step 2: Q is second to left of R → Position 3.
- Step 3: P is immediate neighbor of Q → Position 2 or 4.
- Step 4: S doesn't sit at ends → S is in Position 2, 3, or 4. Position 3 is Q's. So S is at 2 or 4.
- Step 5: If P is at Position 2, then S must be at Position 4. T gets Position 1. ✓
- Step 6: If P is at Position 4, then S must be at Position 2. T gets Position 1. ✓
Both cases give T at Position 1 (left end).
Answer: T sits at the left end.
Example 2: Circular Arrangement
Problem: Six persons A, B, C, D, E, F sit around a circular table facing the center.
- A sits second to the right of D.
- B sits opposite to A.
- C is an immediate neighbor of both A and D.
- E is not a neighbor of B.
Find: Who sits opposite to D?
Solution:
- Step 1: Place D anywhere (say at 12 o'clock position).
- Step 2: A is second to right of D → A at 4 o'clock.
- Step 3: B is opposite A → B at 10 o'clock.
- Step 4: C is neighbor of both A and D → C must be between them at 2 o'clock.
- Step 5: Remaining positions: 6, 8 o'clock for E and F.
- Step 6: E is not neighbor of B. B's neighbors are positions at 8 and 12. 12 is D. So 8 o'clock cannot be E → 8 o'clock = F, 6 o'clock = E.
- Step 7: D (12 o'clock) is opposite to 6 o'clock = E.
Answer: E sits opposite to D.
Common Mistakes
- Ignoring facing direction → Students apply left-right rules for "facing center" when persons face outside. Always confirm direction before drawing.
- Treating "to the left" as "immediately to the left" → "A sits to the left of B" allows gap between them unless "immediately" is stated. Read clues word-by-word.
- Fixing positions too early → Placing a person definitively when the clue allows multiple spots leads to wrong diagrams. Keep options open with Case 1/Case 2 notation.
- Miscounting in circular → In circular, students often miscount "second to the right" because they forget to skip the immediate neighbor. Practice counting: immediate = 1, next = 2.
- Forgetting to verify → After completing the arrangement, not cross-checking all conditions. Spend 10 seconds verifying each clue against final diagram.
Quick Reference
- Linear: Always note facing direction—it determines left/right meaning.
- Circular facing center: Person's right = your left when looking at them.
- Start with definite clues (end positions, exact placements) first.
- "Second to the right" = skip one, land on the second.
- "Opposite" in circular of n persons = n/2 positions away.
- When stuck, draw multiple cases and eliminate with remaining clues.