Assam PSC – Reasoning Ability (Puzzles)
Target: IIT‑JEE / competitive level rigor
Focus: Logical deduction, systematic elimination, and speed
1. Why Puzzles Matter
- Cognitive skill: trains short‑term memory, pattern recognition, and deductive reasoning.
- Exam pattern: 15–20 puzzles per paper, 1–2 min each → time management is key.
- Common trick: The word “between” vs “not between”, “immediately after” vs “after”, “next to” vs “anywhere next”.
2. Types of Puzzles & Typical Constraints
| Category | Typical Constraints | Key Logical Tools |
|---|---|---|
| Seating / Arrangement | “A sits to the left of B”, “C is not next to D”, “E is between F & G” | Row/Column indexing, adjacency rules, relative position |
| Time & Sequence | “X started 2 h after Y”, “Z finished before W”, “Sequence of events” | Chronological ordering, time arithmetic |
| Number / Pattern | “The third number is double the first”, “Missing value in arithmetic progression” | Algebraic expressions, modular arithmetic |
| Object/Attribute | “The boy wearing blue has a red book”, “The man with a cat has a bike” | Attribute matching, bipartite matching |
| Hybrid | Combines two or more of the above | Layered reasoning, cross‑referencing |
3. General Strategy (Step‑by‑Step)
Step 1 – Extract and Tabulate
Write down every explicit statement.
For seating: create a table (rows/columns).
For time: create a timeline or order list.
Step 2 – Identify the “Anchor”
Pick the statement with the most restrictive condition (e.g., “A is exactly in the center”, “C sits next to B and D”).
Place it first; it reduces the search space.
Step 3 – Apply “Elimination”
For each remaining entity, list possible positions or time slots and cross‑out those that conflict with the anchor.
Step 4 – Use “Contradiction”
Assume a placement; see if it leads to a conflict with any other rule.
If yes → discard that assumption.
Step 5 – Iterate
Repeat until all entities satisfy all constraints.
Step 6 – Verify
Check each rule once more.
If any rule is violated → backtrack to the last decision point.
4. Important Formulae & Notations
| Topic | Formula | Use‑Case |
|---|---|---|
| Permutation | ( P(n,k) = \frac{n!}{(n-k)!} ) | Number of ways to arrange k distinct items in n places |
| Combination | ( C(n,k) = \frac{n!}{k!(n-k)!} ) | Choosing k items from n (no order) |
| Relative Position | If (A) is n places to the left of (B): ( \text{Pos}(B) = \text{Pos}(A) + n ) | For linear seating |
| Time Arithmetic | If event (X) starts t hours after (Y): ( \text{Start}(X) = \text{Start}(Y) + t ) | For scheduling puzzles |
| Modulo (for cyclic seating) | ( (\text{Pos}(A) + n) \bmod N ) | For circular tables |
Tip: In many puzzles, the exact value of a number or time is irrelevant; only the relative ordering matters.
5. Tricky Points & Common Mistakes
| Trick | Explanation | What to Watch Out For |
|---|---|---|
| “Between” vs “Not Between” | “A is between B and C” → A is exactly somewhere between B and C with no other entity in between. “A is not between” allows any position outside that interval. | Don’t assume “between” = “adjacent to one of the two” |
| “Immediately After” vs “After” | “X immediately after Y” → X starts right after Y ends. “X after Y” → X starts any time after Y. | Misplacing a 1‑hour buffer can flip the whole ordering |
| Circular Arrangements | Positions wrap around. The left of the first seat is the last seat. | Forgetting the modulo operation leads to wrong counts |
| Counting vs. Placement | Number of ways ≠ the only possible arrangement. | A puzzle may ask which of the following is true; you must find the unique arrangement, not count them all. |
| Redundant Information | Sometimes extra statements are given. They can confirm a deduction or distract. | Don’t waste time on checking every statement; focus on the constraints that restrict choices. |
| Assumption Bias | Choosing an entity arbitrarily as “first” can lead to wrong conclusions if not justified. | Always |