IBPS SO – Reasoning Ability
Topic: Puzzles
What are puzzles?
Puzzles are a group of reasoning questions where information is given in the form of statements, conditions, or patterns.
Your job is to figure out the missing piece of information (a person, a number, a position, etc.) that satisfies all the given conditions.
1. Simple Explanation
| Step | What to do | Why? |
|---|---|---|
| 1️⃣ | Read the question carefully | Every statement may contain a key constraint. |
| 2️⃣ | Identify variables | People, objects, numbers, positions, times, etc. |
| 3️⃣ | Create a table/diagram | Visual representation eliminates confusion. |
| 4️⃣ | List all given constraints | Write them as simple equations or inequalities. |
| 5️⃣ | Iterate & eliminate | Use “fitting” or “checking” to remove impossible options. |
| 6️⃣ | Find the answer | Once all constraints are satisfied, the answer emerges. |
2. Key Points (Quick Checklist)
| # | Key Point | Example |
|---|---|---|
| 1 | Positions matter – use 1,2,3… or A,B,C… | “The second person from the left is….” |
| 2 | Relative positions – who is left/right/above/below | “X is sitting between Y and Z.” |
| 3 | Numerical constraints – sums, differences, multiples | “The age difference between A and B is 5 years.” |
| 4 | Logical elimination – rule out possibilities that violate any clue | If clue A says “Person X is not at the extreme edge,” eliminate edges. |
| 5 | Cross‑checking – verify that every clue is satisfied | After filling the table, walk through each clue again. |
| 6 | Multiple correct answers? – If more than one solution possible, check if the question asks for “the most probable” or “any” | “Find the position of X.” |
3. Worked Example
Question
Five people – A, B, C, D, E – are seated in a row, left to right.
Conditions:
- B is to the right of A.
- D is to the left of C.
- B is not adjacent to C.
- E sits at one end.
- C sits immediately to the right of B.
Find the seating arrangement.
Step‑by‑Step Solution
| Step | Action | Result |
|---|---|---|
| 1️⃣ | Create a 5‑slot table: `1 | 2 |
| 2️⃣ | Place E at an end (slot 1 or 5). | Two possibilities: E _ _ _ _ or _ _ _ _ E. |
| 3️⃣ | From clue 5, C sits immediately to the right of B → B is immediately left of C. | This pair can be (B,C) in slots (1,2), (2,3), (3,4), or (4,5). |
| 4️⃣ | From clue 1, B is to the right of A → A must be left of B. | So A cannot be in slot 5 (since B would then be to the right of A). |
| 5️⃣ | From clue 3, B not adjacent to C – contradicts clue 5! Wait! | Indeed, clue 3 “B is not adjacent to C” cannot coexist with clue 5 “C sits immediately to the right of B.” → There is a typo or mis‑reading. Usually the puzzle states B is adjacent to C or B is not adjacent to D. Let's correct: assume clue 3 should read B is not adjacent to D (common pattern). |
| 6️⃣ | Re‑evaluate with corrected clue: B not adjacent to D. | Keep track of pair (B,C). |
| 7️⃣ | Try arrangement 1: E B C _ _ (B in 2, C in 3). |
Remaining slots 4,5 for A and D. |
| 8️⃣ | From clue 2, D left of C → D must be in slot 1 or 2 or 3. But slot 1 is E, slot 2 is B, slot 3 is C. No slot left → reject. | |
| 9️⃣ | Try arrangement 2: E _ B C _. |
Slots used: 1 = E, 3 = B, 4 = C. |
| 10️⃣ | Remaining slots: 2,5 for A & D. D must be left of C (slot < 4). So D can be slot 2. | A gets slot 5. |
| 11️⃣ | Final arrangement: E D B C A. |
Check all clues: 1) B (slot 3) right of A (slot 5) → NO (B is left of A). |
We made mistake again: clue 1 says B is to the right of A, so A must be left of B. In arrangement E D B C A, A is right of B → wrong.
Let's restart from scratch with a systematic approach:
Systematic Approach
- Place E at an end: choose slot 1 (E _ _ _ ) or slot 5 ( _ _ _ E).
- Place (B,C) pair: since C immediately right of B, possible pairs are (1,2), (2,3), (3,4), (4,5). But if E occupies slot 1, B cannot be slot 1; similarly if E occupies slot 5, C cannot be slot 5.
Case A: E at slot 1
-
B cannot be slot 1 → B can be 2,3,4.
-
C must be B+1.
- If B=2 → C=3.
- If B=3 → C=4.
- If B=4 → C=5.
-
From clue 3 (B not adjacent to D) → D cannot be B±1.