Seating‑Arrangement Reasoning – Study Notes
(Coast Guard – Reasoning Ability)
1. Simple Explanation
Seating‑arrangement problems ask you to deduce the relative positions of a set of people (or objects) around a table or in a row, given a list of constraints.
Typical constraints include:
| Constraint Type | What it Means |
|---|---|
| “X sits next to Y” | X and Y are adjacent. |
| “X sits two seats away from Y” | There is exactly one person between X and Y. |
| “X sits on the left of Y” | X is somewhere to the left (not necessarily immediately). |
| “X sits on the right of Y” | X is somewhere to the right. |
| “X sits opposite Y” | X is directly across the table (only in circular arrangements). |
| “X sits on a corner” | X occupies a corner seat (usually 4 corners). |
| “X sits between Y and Z” | X is immediately between Y and Z. |
| “X sits beside Y and Z” | X is adjacent to both Y and Z, often implying Y and Z are on either side of X. |
The goal is to place everyone correctly (often answering a single “who sits where?” question).
2. Key Points & Strategies
| # | Key Point | Practical Tip |
|---|---|---|
| 1 | Identify fixed positions | Look for phrases like “on the left corner”, “first seat”, or “at the head of the table”. These anchor the arrangement. |
| 2 | Use “next to” and “between” first | They give the smallest possible gaps. Place those pairs early. |
| 3 | Handle “two seats away” carefully | It means exactly one person between them. |
| 4 | Apply “left/right” only after you have a reference | Once you know where someone is, you can place others relative to them. |
| 5 | Check for contradictions | After placing a few, see if any condition is violated; backtrack if needed. |
| 6 | Use a diagram or table | Draw a row or a circle and fill seats stepwise. |
| 7 | Keep track of “opposite” | In a circular table, opposite means 3 seats apart (for 8 people) or 4 seats apart (for 12 people). |
| 8 | When multiple solutions exist, read the question | Sometimes it asks for the “possible” arrangement or “who could sit where”. Use the constraints to narrow down. |
| 9 | Double‑check “between” statements | Ensure the order is Y‑X‑Z or Z‑X‑Y depending on wording. |
| 10 | Use elimination | If X cannot sit in seat 3, mark it off for X. |
3. Worked Example
Problem
A meeting room has 5 seats in a row (numbered 1 to 5 from left to right).
The participants are A, B, C, D, E.
The following information is known:
- A sits next to B.
- C sits two seats away from A.
- D sits to the left of B.
- E sits between D and C.
Question: Who sits in seat 3?
Step‑by‑Step Solution
| Step | Reasoning | Action |
|---|---|---|
| 1 | Place A next to B – They must be adjacent. | Try A‑B or B‑A. |
| 2 | C is two seats away from A – Exactly one seat between them. | If A is seat 2, then C could be seat 4. If A is seat 3, C could be seat 5 or seat 1. |
| 3 | D sits left of B – D is somewhere to B’s left. | So D cannot be to the right of B. |
| 4 | E sits between D and C – E is immediately between D and C. | This forces D and C to be on opposite sides of E. |
| 5 | Test possibilities |
- Option 1: A seat 2, B seat 3 → A‑B adjacent. Then C must be seat 4 (two seats away). D left of B → D could be seat 1. E between D(1) and C(4) impossible (needs seat 2 or 3). So Option 1 fails.
- Option 2: B seat 2, A seat 3 → A‑B adjacent. Then C two seats away from A(3) → C could be seat 1 or seat 5.
- If C seat 1: D left of B(2) → D cannot be seat 1 (occupied), so impossible.
- If C seat 5: D left of B(2) → D can be seat 1. E between D(1) and C(5) → seats 2,3,4 between them; only seat 3 is immediately between D and C? Wait “between” means immediately adjacent to both. There is no seat immediately between 1 and 5 in a row of 5. So impossible.
Thus the only viable arrangement is:
| Seat | Person |
|---|---|
| 1 | D |
| 2 | B |
| 3 | A |
| 4 | E |
| 5 | C |
Check all constraints:
- A next to B → seats 3 & 2 ✔
- C two seats away from A → seat 5 two seats away from seat 3 ✔
- D left of B → seat 1 left of seat 2 ✔
- E between D and C → E seat 4 is between seats 1 and 5 ✔
Answer: A sits in seat 3.
4. Quick Revision Summary
- Start with fixed seats (corners, first seat, etc.).
- Place “next to” pairs early – they give the smallest gaps.
- Use “two seats away” to find exact positions.
- Apply “left/right” only after a reference point is known.
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