SSC MTS – Reasoning Ability
Topic – Puzzles
Puzzles are a cornerstone of the Reasoning section.
They test logical deduction, pattern recognition, spatial reasoning, and the ability to synthesize information quickly.
1. What Are Puzzles?
| Type | Description | Typical Questions |
|---|---|---|
| A. Seating / Arrangement | People/objects placed in a line, on a bench, or in a room. | “Mr. K sits between Mr. L and Mr. M.” |
| B. Time / Sequence | Events happening on a clock, calendar, or in a given order. | “If the third event starts at 2 pm, when does the fifth start?” |
| C. Spatial / Grid | Items placed on a grid or in a room; often with directional clues. | “The book is to the left of the cup.” |
| D. Word/Number | Clues based on letters, numbers, or patterns. | “X is the fifth letter in the alphabet.” |
| E. Logical Deduction | Non‑spatial reasoning involving true/false statements. | “If A is true, then B is false.” |
| F. Combination | Two or more of the above combined. | “Arrange 5 people in a circle and then determine the order of their tasks.” |
Key Idea: Every puzzle has a single consistent arrangement that satisfies all clues.
2. General Problem‑Solving Strategy
| Step | What to Do | Why It Works |
|---|---|---|
| 1. Read All Clues Once | Take a quick skim. | Avoid missing any constraint. |
| 2. Identify Fixed Points | Look for clues that give absolute positions (e.g., “Mrs. X sits at the far left”). | Pinning one item reduces the search space. |
| 3. Create a Skeleton | Draw a table/graph/blank grid with rows = items, columns = positions. | Visual aid speeds up deduction. |
| 4. Mark Definitive Relations | Fill in what is certain (e.g., “A is immediately to the right of B”). | Each filled cell propagates further constraints. |
| 5. Use “Not” Statements | Mark impossible cells (X’s cannot be in position Y). | Eliminates many possibilities quickly. |
| 6. Look for “Only One” Conditions | If a clue says “only one person is older than X”, it forces a unique placement. | Helps break symmetry. |
| 7. Apply Logical Inference | Use if‑then logic: “If X is in Y, then Z must be in W.” | Chain reactions narrow options. |
| 8. Test Possibilities | If still many options, pick a plausible case and test for contradictions. | Contradiction → discard the case. |
| 9. Verify All Clues | Cross‑check the final arrangement against every statement. | Ensures a valid solution. |
| 10. Time Check | Aim to finish within 2–3 minutes per puzzle. | Practice reduces time. |
Tip: Keep a separate “elimination list” for each item (e.g., positions person A can’t occupy).
3. Common Tricky Points
| Tricky Point | How to Spot | Fix |
|---|---|---|
| Direction Ambiguity | “Between” can mean immediately between or anywhere between. | Check if other clues specify “immediately”. |
| Circular vs Linear | “In a circle” vs “in a line”. | For circles, there’s no “first” or “last”; use relative positions only. |
| “Only” vs “At Least One” | “Only one person sits next to X” vs “At least one person sits next to X”. | Count the number of neighboring slots. |
| Simultaneous Conditions | “A is before B and B is before C” – all three must be in that order. | Arrange them sequentially. |
| Hidden Constraints | “If X is in position 3, then Y must be in position 1.” | Treat as a conditional, not a direct placement. |
| Multiple Valid Solutions | Rare, but some puzzles allow two arrangements. | The question will usually ask for “the arrangement” or “the number of possible arrangements”. |
| Negative Statements | “None of the students are older than 20” – a limit on ages. | Keep a separate table for attributes (age, gender, etc.). |
4. Key Logical Patterns & “Formulae”
| Pattern | Example | Quick “Formula” |
|---|---|---|
| Adjacency | “X is immediately to the right of Y.” | X = Y + 1 |
| Between | “X sits between Y and Z.” | Y < X < Z (if linear) |
| Opposite | “X sits opposite Y.” | In a circle: X = Y + n/2 (n = # seats) |
| Distance | “X is 2 seats away from Y.” | |
| Constraint Propagation | “If X is in position 1, Y must be in position 4.” | X=1 → Y=4 |
| Permutation Count | “All 5 items can be arranged in 5! ways.” | 5! = 120 |
Remember: In puzzles you rarely calculate factorials; instead you eliminate until one arrangement remains.
5. Worked Mini‑Example
Clues
- Three persons (A, B, C) sit in a row.
- A sits to the left of B.
- C sits between A and B.
- B does not sit at an end position.
Solution
| Position | 1 | 2 | 3 |
|---|---|---|---|
| Person | A | C | B |