Puzzles: Notes और MCQ Practice

आसान भाषा में

Puzzles Reasoning section का वह हिस्सा है जहाँ multiple variables (जैसे Persons, Floors, Days, Colors, Professions) को दी गई conditions के अनुसार arrange या map करना होता है। RRB NTPC में Floor-based, Scheduling (Days/Months), Box-based और Tabular Puzzles के 3 से 5 questions का set अक्सर पूछा जाता है। यह purely reading skills, accurate representation और logical connectivity का खेल है!

Important Rules & Strategy

• Fix the Base: Days (Mon-Sun), Months, या Floor numbers (1 to 7) naturally fixed होते हैं, इन्हें हमेशा table का base (fixed column) बनाएं।
• Start with Definite Clues: सबसे पहले direct statements भरें (जैसे: "P lives on the 4th floor")।
• Note Negative Clues: जो information 'नहीं' है (जैसे: "Q does not like Blue"), उसे table के बगल में cross (✗) mark के साथ short form में लिखें।
• Link Related Statements: Definite clues भरने के बाद उन्हीं variables से जुड़े indirect clues को connect करते जाएं।

2 Quick Tricks

1. Parallel Possibilities (2-Case Method): अगर किसी clue में दो options बन रहे हों (जैसे A top पर है या bottom पर), तो दिमाग में solve करने के बजाय तुरंत Case 1 और Case 2 parallel बना लें। आगे चलकर गलत Case naturally eliminate हो जाएगा।
2. Short-hand Notation: पूरी line बार-बार पढ़ने के बजाय standard symbols use करें; जैसे: $A$ sits above $B$ $\rightarrow$ A ↑ B, Immediate neighbor $\rightarrow$ AB, Opposite $\rightarrow$ A ↔ B।

2 Common Mistakes

1. Self-Assumption: अपनी तरफ से relations या gender assume न करें। जब तक strictly confirm न हो, किसी variable को fix न मानें।
2. Single Diagram Trap: एक ही diagram में बार-बार strike-through या erase करने की गलती मत कीजिए, इससे rough sheet messy हो जाती है और time waste होता है।

Puzzles (General Intelligence and Reasoning)

1. Concept

In competitive exams like RRB NTPC, Puzzles test your analytical thinking, data comprehension, and spatial arrangement abilities.

A puzzle presents a set of raw, unstructured conditions involving multiple entities (people, days, months, floors, boxes, colors, professions). Your task is to organize this scattered information into a structured, logical format (typically a table or vertical/horizontal diagram) to establish exact relationships between all given elements.

Common Types of Puzzles in RRB NTPC:

1. Floor-based Puzzles: People living on different numbered floors of a multistory building.
2. Box / Stack Puzzles: Boxes placed one above another in a vertical stack.
3. Scheduling Puzzles: Events or visits scheduled across days of the week, months, or specific dates.
4. Classification / Tabular Puzzles: Matching 3 or more attributes (e.g., Person + City + Profession + Favorite Color).

2. Important Rules, Terms, and Facts

Key Positional Terms

• "Between A and B": If 2 people are between A and B, there are exactly 2 slots separating them (Gap = 2). For floors: Floor number difference = Gap + 1 = 3.
• "X is 2 floors above Y": This means Floor(X) − Floor(Y) = 2. There is only 1 floor between X and Y.
• "Immediately Above / Below": Zero gap between the two entities (they are adjacent).
• "A lives on an even-numbered floor": If floors are 1 to 7, possible floors are 2, 4, or 6.

Conventions and Structural Rules

• Standard Floor Convention: Unless stated otherwise, the bottom-most floor is Floor 1, the floor above it is Floor 2, and the top-most floor is the highest number (e.g., Floor 7).
• Base Variable Selection: Always choose a fixed sequence as your anchor/base column:
• Days of the week: Monday → Saturday / Sunday
• Floors: Top floor → Bottom floor (or 1 to N)
• Months: Chronological calendar order
• Definite vs. Conditional Clues:
• Definite clues give a fixed spot (e.g., "M visits on Wednesday"). Fill these first.
• Relative clues link two entities (e.g., "P sits 2 places away from Q"). Use them once a base anchor is set.
• Negative clues tell where someone CANNOT go (e.g., "R does not live on floor 3"). Mark these beside the row/column with a cross (×).

3. Solved Examples (Exam Style)

Example 1: Floor-Based Puzzle

Question: Seven persons—P, Q, R, S, T, U, and V—live on separate floors of a 7-storey building. The ground floor is numbered 1, the floor above it is 2, and so on, up to the top floor numbered 7.

• T lives on an odd-numbered floor above floor 4.
• Exactly two persons live between T and P.
• Q lives immediately above P.
• Only one person lives between Q and R.
• S lives on an odd-numbered floor.
• U lives on a floor above V.

Who lives on Floor 6?

Step-by-Step Solution:

Step 1: Create a vertical frame from floor 7 down to floor 1.

Floor — Person

7 —

6 —

5 —

4 —

3 —

2 —

1 —

Step 2: Apply clue 1: T lives on an odd floor above floor 4. Odd floors above 4 are 5 and 7.

• Case 1: T is on Floor 5.
• Case 2: T is on Floor 7.

Step 3: Apply clue 2: Exactly two persons live between T and P.

• In Case 1 (T = 5): P must be on Floor 2 (two floors: 3 and 4 between them).
• In Case 2 (T = 7): P must be on Floor 4 (two floors: 5 and 6 between them).

Step 4: Apply clue 3: Q lives immediately above P.

• In Case 1 (P = 2): Q is on Floor 3. (Valid)
• In Case 2 (P = 4): Q is on Floor 5. (Valid)

Step 5: Apply clue 4: Only one person lives between Q and R.

• In Case 1 (Q = 3): R can be on Floor 1 or Floor 5. But Floor 5 is occupied by T. Thus, R must be on Floor 1.
• In Case 2 (Q = 5): R can be on Floor 3 or Floor 7. Floor 7 is occupied by T, so R is on Floor 3.

Step 6: Apply clue 5: S lives on an odd-numbered floor.

• In Case 1: Remaining floors are 4, 6, and 7. The only odd floor remaining is 7. So, S is on Floor 7.
• In Case 2: Remaining floors are 1, 2, and 6. Odd floor is 1, so S = 1. Remaining floors: 2, 6.

Step 7: Apply clue 6: U lives on a floor above V.

• In Case 1: Floors left are 6 and 4. Since U is above V, U is on Floor 6 and V is on Floor 4.
• In Case 2: Let us re-verify all conditions: Both cases work unless further constrained, but Case 1 creates the clear valid distribution:
• Floor 7: S
• Floor 6: U
• Floor 5: T
• Floor 4: V
• Floor 3: Q
• Floor 2: P
• Floor 1: R

Answer: U lives on Floor 6.

Example 2: Box Stacking Puzzle

Question: Six boxes—A, B, C, D, E, and F—are stacked one above the other in a rack, numbered 1 (bottom) to 6 (top).

• Box D is placed at an even-numbered position.
• Two boxes are kept between Box D and Box A, where Box A is placed above Box D.
• Box F is placed immediately below Box A.
• Only one box is placed between Box F and Box C.
• Box B is placed at some position above Box E.

Which box is placed at position 3?

Step-by-Step Solution:

Step 1: Define the frame from 6 (top) to 1 (bottom).

Step 2: Box D is at an even position (2, 4, or 6). Box A is above Box D with two boxes between them.

• If D = 4, A would have to be at position 4 + 3 = 7 (Impossible, only 6 boxes exist).
• If D = 6, A cannot be above D.
• Therefore, D must be at position 2.
• Since 2 boxes are between D and A, A is at position 5 (positions 3 and 4 are between them).

Step 3: Box F is immediately below Box A.

• Since A = 5, F is at position 4.

Step 4: Only one box is between Box F and Box C.

• F is at 4. The box with 1 gap can be at position 2 or position 6.
• Position 2 is already occupied by D.
• Therefore, C is at position 6.

Step 5: Box B is somewhere above Box E.

• Unoccupied positions: 1 and 3.
• Since B is above E: B is at position 3, and E is at position 1.

Final Arrangement:

• Position 6: Box C
• Position 5: Box A
• Position 4: Box F
• Position 3: Box B
• Position 2: Box D
• Position 1: Box E

Answer: Box B is placed at position 3.

Example 3: Day-Based Scheduling Puzzle

Question: Six friends—J, K, L, M, N, and O—attend a training session on six different days of the same week, from Monday to Saturday.

• M attends on Wednesday.
• L attends on the day immediately after M.
• Two persons attend between L and O.
• N attends on the day immediately after O.
• K attends on one of the days before J.

Who attends the session on Saturday?

Step-by-Step Solution:

Step 1: Fix the days of the week in chronological order.

• Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.

Step 2: Place definite clues:

• "M attends on Wednesday" → Wednesday: M
• "L attends immediately after M" → Thursday: L

Step 3: "Two persons attend between L and O":

• L is on Thursday. Two persons between them means 2 days gap.
• Going downward: Friday and Saturday would leave no space for O.
• Going upward: Tuesday and Wednesday are the two days. Hence, Monday: O.

Step 4: "N attends immediately after O":

• O is on Monday, so Tuesday: N.

Step 5: Remaining days are Friday and Saturday. The remaining persons are K and J.

• "K attends on one of the days before J" → Friday: K and Saturday: J.

Final Schedule:

• Monday: O
• Tuesday: N
• Wednesday: M
• Thursday: L
• Friday: K
• Saturday: J

Answer: J attends the session on Saturday.

Example 4: Tabular / Attribute Matching Puzzle

Question: Four friends—P, Q, R, and S—live in four different cities (Delhi, Mumbai, Kolkata, Chennai) and like four different colors (Red, Blue, Green, Yellow).

• P lives in Delhi and does not like Red or Yellow.
• The person who lives in Chennai likes Yellow.
• R likes Blue but does not live in Mumbai.
• S does not live in Chennai.

Which city does S live in, and what color does S like?

Step-by-Step Solution:

Step 1: Create a 4-row grid with columns: Person, City, Color.

Step 2: Clue 1: P lives in Delhi. P does not like Red or Yellow.

• P's color can only be Blue or Green.

Step 3: Clue 3: R likes Blue.

• Since R likes Blue, P cannot like Blue.
• Therefore, P likes Green.

Step 4: Clue 3 continued: R lives in neither Mumbai nor Delhi (P is in Delhi).

• So R lives in either Kolkata or Chennai.
• Clue 2 says: The person in Chennai likes Yellow. But R likes Blue! Thus, R cannot live in Chennai.
• Therefore, R lives in Kolkata.

Step 5: Determine cities for Q and S:

• Remaining cities: Mumbai and Chennai.
• Clue 4: S does not live in Chennai.
• Therefore, S lives in Mumbai, which leaves Q living in Chennai.

Step 6: Determine colors:

• Chennai resident likes Yellow → Q likes Yellow.
• Remaining color for S: Red.

Final Table:

Person — City — Color

P — Delhi — Green

Q — Chennai — Yellow

R — Kolkata — Blue

S — Mumbai — Red

Answer: S lives in Mumbai and likes Red.

4. Shortcuts and Speed Tricks

1. Shorthand Notation: Save time by noting conditions in short symbols on your scratch sheet:

• A ↑ B = A is above B
• A / B = A and B are adjacent
• A (2) B = Exactly 2 people between A and B
• X ≠ Floor 3 = X does not live on Floor 3

1. The Parallel Case Method: Never erase your work when faced with two possibilities. Draw Case 1 and Case 2 side-by-side. As you apply subsequent clues, the wrong case will automatically violate a rule and get eliminated.
2. Anchor First: Never begin with isolated clues like "A lives near B." Always start with the entity that fixes the grid (e.g., "R is on Floor 4" or "Tuesday is Lecture X").
3. Check the Negatives: When stuck, look at negative clues (e.g., "neither X nor Y"). They drastically narrow down remaining slots.

5. Common Mistakes to Avoid

• Confusing Gap vs. Floor Difference:
• "X is 3 floors above Y" means Floor(X) − Floor(Y) = 3 (There are 2 floors between them).
• "There are 3 floors between X and Y" means Floor(X) − Floor(Y) = 4.
• Assuming Top/Bottom Orientation: Do not assume Box 1 is at the top unless the question explicitly states it. Standard convention is 1 at the bottom, but always read the numbering rule given in the prompt.
• Ignoring "Immediately": Treating "A is above B" as "A is immediately above B". "Above" can mean anywhere higher up.
• Over-investing Time: In RRB NTPC, if a puzzle does not untangle within 2 to 2.5 minutes, mark it for review and move on. Getting stuck ruins time management for easier arithmetic and general awareness sections.