Odisha TET – Reasoning Ability
Puzzles
(Rigorous, exam‑oriented notes for IIT‑JEE/competitive style)
1. Introduction
Puzzles form one of the most challenging sections of the Reasoning Ability paper.
They test deductive reasoning, patterns, spatial visualization and sometimes
basic combinatorics. The key to success is to:
- Classify the puzzle type quickly.
- Apply a systematic strategy for that type.
- Eliminate impossibilities using logical inference.
- Check the solution against all constraints.
Below we give a concise strategy guide, formulae, common pitfalls and a hard practice question.
2. Typology of Puzzles
| # | Puzzle Type | Typical Features | Strategy |
|---|---|---|---|
| 1 | Seating / Arrangement | Positions, relative order, constraints (“A sits next to B”, “C is 3rd from left”) | Draw a linear or circular table; mark fixed positions; use elimination. |
| 2 | Sequence / Pattern | Numerical/letter sequences, rules (“next term is sum of two preceding”) | Identify rule by testing candidates; use algebraic form if possible. |
| 3 | Spatial & Grid | 2‑D arrays, boxes, crossword‑style | Visualize grid; use color‑coding to mark possibilities. |
| 4 | Logical Deduction | “If X then Y” statements, often presented in tables | Build a truth table or a deduction grid. |
| 5 | Number & Arithmetic | Arithmetic operations, inequalities | Simplify inequalities; use bounds; check parity. |
| 6 | Word & Language | Anagrams, synonym/antonym clues | Use letter frequency; form words that satisfy all clues. |
| 7 | Time & Distance | Speed, distance, time, rate problems | Use ( \text{Time} = \frac{\text{Distance}}{\text{Speed}} ). |
| 8 | Mixed‑Constraint | Combine above features | Treat each sub‑constraint independently then merge. |
Tip: In TET, most puzzles are linear arrangements or simple sequences.
For multi‑constraint puzzles, isolate each clue and treat it as a separate sub‑problem.
3. Systematic Strategies
3.1 Arrangement Puzzles
-
Fix Anchors
- Identify any item with a fixed position (e.g., “The teacher in the 3rd seat from left is …”).
- Mark it on a line of empty boxes.
-
Use Relative Orders
- Translate statements like “X sits between Y and Z” into inequalities.
- If the order is “left of” or “right of”, set up a partial order.
-
Apply the Pigeonhole Principle
- If there are more items than positions, some must share a position.
- Useful when constraints are “exactly two people sit together”.
-
Back‑tracking
- After fixing a few positions, try a candidate for the next item.
- If a contradiction appears, backtrack and try another.
-
Scanning for Contradictions
- After each placement, check all constraints.
- If any is violated, discard the branch immediately.
3.2 Sequence Puzzles
-
Identify the Domain
- Are the terms integers, letters, dates, etc.?
- This may limit possible operations (e.g., only integer operations).
-
Test Simple Recurrence
- Assume a linear recurrence (a_{n} = p a_{n-1} + q a_{n-2}).
- Solve for (p,q) using the first few terms.
-
Check for Injective/Surjective Constraints
- If the puzzle states “all terms are distinct”, eliminate candidates that repeat.
-
Use Modular Arithmetic
- For patterns involving remainders (e.g., “next term ≡ 2 (mod 3)”), test the residue classes.
-
Look for Symmetry
- Palindromic, arithmetic progression, or geometric progression hints.
3.3 Logical Deduction
-
Truth Table
- For each statement, create a column of possible truth values.
- Apply logical operators to eliminate impossible combinations.
-
Deduction Grid
- Draw