📚 Madhya Pradesh TET – Reasoning Ability
Topic: Seating Arrangement
Why it matters
The seating arrangement section tests your ability to interpret constraints, build a mental model, and deduce the final order. It is a staple of most reasoning tests (TET, JEE‑Mains, UPSC, etc.) and the easiest to crack once you know the patterns.
1️⃣ Simple Explanation
A seating arrangement problem gives you a set of individuals and a list of constraints (e.g., “A sits to the left of B”, “C is between D and E”, “F sits opposite G”).
Your task: determine the relative positions of everyone.
- Positions can be horizontal (left‑right), vertical (front‑back), or circular (around a table).
- Constraints are usually exclusive (exactly one position) or inclusive (possible positions).
- The answer may require you to find the exact seat of a particular person or to fill a table with all seats.
2️⃣ Key Points & Strategy
| # | Concept | How to Apply | Quick Tip |
|---|---|---|---|
| A | List every person & seat | Create a blank table or diagram. | Use a grid for linear arrangements; use a circle diagram for round tables. |
| B | Categorize constraints | Separate fixed (e.g., “X sits third from left”) from relative (e.g., “Y sits next to Z”). | Mark “fixed” constraints first – they anchor the puzzle. |
| C | Work from extremes | Determine who sits at the far left/right or front/back. | “Leftmost” or “rightmost” clues are usually unique. |
| D | Use elimination | If a person has only one possible spot left, place them. | Keep a list of “possible spots” for each person; shrink it as you place others. |
| E | Check consistency | After placing a person, verify all existing constraints. | If a contradiction appears, backtrack. |
| F | Count the number of seats | The number of individuals equals the number of seats; no one sits twice. | If given a “between” constraint, remember it uses exactly one seat between. |
| G | Look for “unique” patterns | E.g., “X sits between Y and Z” → X is immediately in the middle. | If “between” is not “immediately”, it still means X is exactly between Y and Z, with one seat between each. |
| H | Remember “opposite” | In circular arrangements, opposite means half the seats away. | For 4 seats, opposite = 2 seats away; for 6 seats, opposite = 3 seats away. |
| I | Use “next to” vs “adjacent to” | “Next to” implies immediate adjacency; “adjacent to” is the same. | If the puzzle is linear, “next to” means one seat away. |
General tip: Start with the most restrictive clues (those that limit positions the most). They usually involve exact positions or unique relative positions.
3️⃣ Worked Example
Problem (adapted from a typical TET question)
There are 8 students – A, B, C, D, E, F, G, H – seated in a single row of 8 seats (from left to right). The following constraints apply:
- A sits exactly 2 seats to the left of C.
- B sits to the immediate right of D.
- E sits between A and H.
- F sits in the middle seat of the row.
- G sits somewhere to the right of H but left of B.
- C sits immediately to the left of G.
Question: Determine the seating order from left to right.
Step‑by‑Step Solution
| Step | Action | Reasoning |
|---|---|---|
| 1 | Place F | “F sits in the middle seat” → seat 4 (since 8 seats, middle seats are 4 & 5; but only one middle → seat 4). |
| 2 | Use Constraint 1 | A is 2 seats left of C → possible pairs: (A,B) at seats 1‑3, (B,C) at 2‑4, etc. Since F is at 4, C cannot be seat 4. |
| 3 | Place B and D | “B sits to the immediate right of D” → B after D. |
| 4 | Place G relative to H | “G sits somewhere to the right of H but left of B” → G is between H and B. |
| 5 | Place C relative to G | “C sits immediately to the left of G” → C = G-1. |
| 6 | Combine 1 & 5 | A is 2 seats left of C, and C is left of G. |
| 7 | Check E | “E sits between A and H” → A < E < H. |
| 8 | Try a concrete assignment | Let’s try A at seat 1 → then C at seat 3 (since C = A+2). |
| 9 | Place G |