Seating Arrangement – Reasoning Ability
(AWS Certification – Reasoning Ability Section)
1. Simple Explanation
A seating‑arrangement problem asks you to determine the relative positions of several people (or objects) given a list of constraints such as “X sits immediately to the left of Y” or “Z is two seats away from W.”
The goal is to place everyone in the correct order (or row/column) so that all constraints are satisfied.
Typical settings:
- Linear row – everyone sits in a single line.
- Circular table – everyone sits around a round table.
- Multiple rows – e.g., a classroom or bus seating.
Approach:
- Draw a simple diagram (blank seats or a grid).
- Write each constraint clearly in your own words.
- Apply constraints one by one, using logic and elimination.
- Check consistency after each placement.
2. Key Points & Strategies
| # | Strategy | Why It Works | Example |
|---|---|---|---|
| 1 | Identify fixed points | Fixing one seat (e.g., the first seat or the center) gives a reference for all others. | If “A sits at the leftmost seat,” start from there. |
| 2 | Use “immediately” vs “at least” | Immediate adjacency is stricter than a distance of at least one seat. | “B sits immediately right of C” → B is directly to the right of C. |
| 3 | Count seats between | “Two seats away” means one person between them. | If “D is two seats to the right of E,” D = E + 3 (index). |
| 4 | Apply “left/right” consistently | Keep track of direction relative to a fixed viewpoint (usually left to right). | “F is left of G” → F’s index < G’s index. |
| 5 | Use process of elimination | If a seat can only fit one person after applying all constraints, place it. | When only one spot remains for H, fill it. |
| 6 | Check for contradictions early | If a constraint cannot be met, backtrack. | If A must be both left of B and right of B → impossible. |
| 7 | Draw a table or grid | Visual representation reduces mental clutter. | A 1‑row table of 6 seats, or a 2‑row grid for more complex setups. |
| 8 | Look for “grouping” clues | If two people must sit together, treat them as a mini‑unit. | “I and J sit together” → treat as a block. |
| 9 | Use “distance” constraints to create equations | Translate into algebraic relations (index numbers). | If “K is 3 seats right of L,” then K = L + 4. |
| 10 | Check end‑points | People at ends have fewer possible neighbors. | “M sits at an end” → only one side neighbor. |
3. Worked Example
Problem
There are 8 people – A, B, C, D, E, F, G, H – seated in a straight line (left to right).
The following conditions apply:
- A sits immediately to the left of B.
- C sits two seats to the right of D.
- E sits third to the left of F.
- G sits at the rightmost seat.
- H sits between A and C.
- No two people with consecutive letters sit together (i.e., A beside B, B beside C, …, G beside H are not allowed).
Find the seating order from leftmost to rightmost.
Step‑by‑Step Solution
| Step | Observation | Action |
|---|---|---|
| 1 | G is rightmost. | Place G in seat 8. |
| 2 | A immediately left of B → A‑B is a block. | A-B occupies two consecutive seats. |
| 3 | H sits between A and C → H is somewhere between the A‑B block and C. | So order is: ... A B ... H ... C ... |
| 4 | C is two seats right of D → D _ C or D _ C with one seat between. | D has to be left of C. |
| 5 | E is third to the left of F → E _ _ F (two seats between). | E left of F. |
| 6 | No consecutive letters adjacent. | A cannot be next to B (but A‑B is forced!), so we must interpret “no two people with consecutive letters sit together” as “no other consecutive pair aside from the mandatory A‑B.” This constraint is violated by the problem unless we treat A‑B as an exception. We'll proceed assuming A‑B is allowed. |
Given the contradictory constraint, we’ll ignore rule 6 for this example (common in exam problems when a rule is too restrictive).
Now build the row:
- Seat 8: G.
- Place A-B block. Since G is at the rightmost, A-B must be somewhere left of G.
- H between A-B and C → So the order must be: A B H C … G.