🧩 Puzzles & Seating Arrangement - Complete Theory

Master arrangement problems - highest weightage in IBPS Reasoning!

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🎯 What are Puzzles & Seating Arrangements?

Puzzles: Logical problems where you arrange people/objects based on given conditions.

Seating Arrangement: Specific type of puzzle involving how people sit in various configurations.

Importance:

• IBPS Prelims: 10-15 questions (30% of reasoning)
• IBPS Mains: 15-20 questions (highest in reasoning)
• Scoring: Can solve 5 questions in 7-8 minutes once you crack the puzzle

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📐 Types of Seating Arrangements

1. Linear Arrangement (Single Row)

Pattern:

People sitting in a straight line, facing North or South

Example: A B C D E ← Facing North

Position: 1 2 3 4 5

Key Points:

• Left/Right depends on facing direction
• If facing North: Left is west side, Right is east side
• If facing South: Left is east side, Right is west side

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2. Linear Arrangement (Double Row)

Pattern:

Two rows facing each other

Row 1: A B C D E (Facing South) ↓ ↓ ↓ ↓ ↓ ↑ ↑ ↑ ↑ ↑ Row 2: P Q R S T (Facing North)

Key Points:

• People in opposite rows face each other
• “Opposite to X” = directly facing X
• Left/Right reverses for opposite directions

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3. Circular Arrangement (Facing Center)

Pattern:

People sitting around a circular table facing the center

    A
H       B

G C F D E

Clockwise: A → B → C → D → E → F → G → H → A

Key Points:

• Right = Clockwise direction
• Left = Anti-clockwise direction
• Immediate right/left = adjacent position
• Opposite = Across the center (for even numbers)

For 8 people:

• Opposite of position 1 = position 5
• Formula: Opposite = Position + (Total/2)

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4. Circular Arrangement (Facing Outside)

Pattern:

    A (facing outward)
H       B

G C F D E

Key Points:

• Right = Anti-clockwise (REVERSED!)
• Left = Clockwise (REVERSED!)
• This is the TRICKY part - direction reverses

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5. Square/Rectangular Table

Pattern:

    Side 1
A       B       C

S4 H D S2 G E

    F
    Side 3

Key Points:

• 4 sides with multiple people per side
• Corner positions vs middle positions
• Facing inside or outside

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6. Floor-Based Puzzle

Pattern:

Floor 8: ___ Floor 7: ___ Floor 6: ___ Floor 5: ___ Floor 4: ___ Floor 3: ___ Floor 2: ___ Floor 1: ___

Key Points:

• People live on different floors
• Above/Below relationships
• Number of floors between people

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🎯 Solving Strategy (Step-by-Step)

Step 1: Read All Conditions (30 sec)

• Scan all conditions quickly
• Identify the most definite condition
• Look for “fixed” positions

Step 2: Identify Master Condition

Master Condition = Most definite/restrictive condition

Examples of Master Conditions:

✓ “A sits at extreme left end” ✓ “Exactly 3 people between A and B” ✓ “A and B sit together” ✓ “Only one person between A and B”

Step 3: Draw the Base Structure

For Linear: Draw the line with positions For Circular: Draw the circle with positions numbered For Floors: Draw vertical structure

Step 4: Place Using Master Condition

Place the most definite elements first.

Step 5: Use Other Conditions

Add remaining elements using other conditions.

Step 6: Fill Remaining Slots

Use logic and elimination.

Step 7: Verify All Conditions

Check if all conditions are satisfied.

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💡 Solved Examples

Example 1: Linear Arrangement (Basic)

Q: 5 people A, B, C, D, E sit in a row facing North. Based on conditions, find the arrangement.

Conditions:

1. A sits at one of the extreme ends
2. B sits second from the right end
3. C sits to the immediate left of B
4. E does not sit at any extreme end

Solution:

Step 1: Draw structure

Position: 1 2 3 4 5

Step 2: Apply Condition 1 (A at extreme)

Case 1: A at left Position: 1 2 3 4 5 Person: A _ _ _ _

Case 2: A at right Position: 1 2 3 4 5 Person: _ _ _ _ A

Step 3: Apply Condition 2 (B second from right = Position 4)

Case 1: Position: 1 2 3 4 5 Person: A _ _ B _

Case 2: Not possible (A already at position 5)

Step 4: Apply Condition 3 (C immediate left of B)

Position: 1 2 3 4 5 Person: A _ C B _

Step 5: Apply Condition 4 (E not at extreme)

Remaining: D, E Positions: 2, 5

E cannot be at 5 (extreme), so E at 2 D at 5

Final: Position: 1 2 3 4 5 Person: A E C B D

Answer: A E C B D

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Example 2: Circular Arrangement (Facing Center)

Q: 6 people P, Q, R, S, T, U sit around a circular table facing the center.

Conditions:

1. P sits second to the left of Q
2. R sits opposite to P
3. S sits immediate right of R
4. T is not adjacent to Q

Solution:

Step 1: Draw circle with 6 positions

    1
6       2

5 3 4

Step 2: Apply Condition 1 (P second left of Q)

If Q at position 1: P is second left = position 5 (1 → 6 → 5 anti-clockwise)

    Q
_       _

P _ _

Step 3: Apply Condition 2 (R opposite P)

P at 5, opposite = 5 + 3 = Position 2

    Q
_       R

P _ _

Step 4: Apply Condition 3 (S immediate right of R)

Immediate right of R (clockwise) = Position 3

    Q
_       R

P S _

Step 5: Remaining T and U

Positions: 4, 6 Condition 4: T not adjacent to Q

Q at 1, adjacent = 2 and 6 Position 2 = R (already filled) Position 6 = cannot be T

So: T at 4, U at 6

Final arrangement: Q(1) U(6) R(2) P(5) S(3) T(4)

Answer: Clockwise from Q: Q, R, S, T, P, U

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Example 3: Floor-Based Puzzle

Q: 7 people A, B, C, D, E, F, G live on 7 floors (1-7) of a building.

Conditions:

1. A lives on 4th floor
2. Only 2 floors between C and A
3. B lives immediately above C
4. E lives on an odd-numbered floor
5. G lives below D but above E
6. F does not live on the topmost floor

Solution:

Step 1: Fixed condition (A on 4th)

Floor 7: ___ Floor 6: ___ Floor 5: ___ Floor 4: A Floor 3: ___ Floor 2: ___ Floor 1: ___

Step 2: Condition 2 (2 floors between C and A)

A on 4, so C can be:

• Floor 1 (4 → 3 → 2 → 1, two floors: 2, 3)
• Floor 7 (4 → 5 → 6 → 7, two floors: 5, 6)

Floor 7: C OR ___ Floor 6: ___ Floor 5: ___ Floor 4: A Floor 3: ___ Floor 2: ___ Floor 1: C OR ___

Step 3: Condition 3 (B immediately above C)

Case 1: C on 1, B on 2 Case 2: C on 7, B on 8 (not possible, max 7 floors)

So: C on Floor 1, B on Floor 2

Floor 7: ___ Floor 6: ___ Floor 5: ___ Floor 4: A Floor 3: ___ Floor 2: B Floor 1: C

Step 4: Remaining D, E, F, G on floors 3, 5, 6, 7

Condition 5: G below D but above E

Order: E < G < D (E lowest, D highest among these three)

Condition 4: E on odd floor

Remaining odd floors: 3, 5, 7 E must be on 3 or 5 (since G and D above E)

If E on 5: G and D need 6, 7 (possible) If E on 3: G and D need 5, 6 OR 5, 7 OR 6, 7 (possible)

Let’s try E on 3: E on 3, then G on 5 or 6, D on 6 or 7

Condition 6: F not on topmost (floor 7)

Remaining: D, E, F, G on 3, 5, 6, 7

If E on 3:

• G and D on upper floors
• F cannot be on 7
• So D must be on 7
• F and G on 5, 6

G above E but below D: G can be 5 or 6 F on remaining

Final: Floor 7: D Floor 6: G Floor 5: F Floor 4: A Floor 3: E Floor 2: B Floor 1: C

Answer: C-B-E-A-F-G-D (bottom to top)

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⚡ Quick Tips & Shortcuts

Tip 1: Use Definite Conditions First

More Definite → Less Definite

Very Definite: ✓ “A sits at extreme left” ✓ “Exactly 3 people between A and B”

Less Definite: ~ “A sits left of B” (could be anywhere left) ~ “A does not sit at extreme” (eliminates only 2 positions)

Tip 2: Circular Table Position Formula

For N people in circle:

• Opposite position = Current + (N/2)
• Immediate right = Current + 1 (clockwise if facing center)
• Immediate left = Current - 1 (anti-clockwise if facing center)

Tip 3: Floor-Based Number Gaps

“2 floors between A and B” means: A on Floor 1 → B on Floor 4 (floors 2, 3 are between)

NOT: A on Floor 1 → B on Floor 3 (only 1 floor between)

Tip 4: Direction Trick

Facing North + “to the right” = East direction Facing South + “to the right” = West direction (reversed!)

Facing Center + “to the right” = Clockwise Facing Outward + “to the right” = Anti-clockwise (reversed!)

Tip 5: Elimination Strategy

If 5 positions and 5 people: After placing 4, the 5th is automatic!

Don’t waste time calculating the last position.

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⚠️ Common Mistakes

❌ Mistake 1: Left-Right Confusion

Wrong: Assuming “left” always means same direction ✗ Right: Check facing direction first! ✓

Facing North: Left = West Facing South: Left = East (reversed!)

❌ Mistake 2: Immediate vs Between

Wrong: “Immediate left” = 1 person between ✗ Right: “Immediate left” = adjacent (NO person between) ✓

“Immediate” = Direct neighbor “One person between” = Gap of 1

❌ Mistake 3: Circular Opposite

Wrong: Opposite in 8-person circle = 3 positions away ✗ Right: Opposite = 4 positions away (N/2) ✓

For odd-numbered circle (e.g., 7 people): There is NO exact opposite position!

❌ Mistake 4: Not Verifying All Conditions

Wrong: Stop after filling all positions ✗ Right: Verify EVERY condition before finalizing ✓

Always cross-check against ALL given conditions!

❌ Mistake 5: Assuming Unique Arrangement

Wrong: There’s only one possible arrangement ✗ Right: Sometimes multiple arrangements are possible ✓

If question asks “which is definitely true?”, only answer what’s true in ALL possible cases.

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📊 Pattern Recognition

Pattern 1: Together/Adjacent

“A and B sit together” OR “A is immediate neighbor of B”

In Linear: A B or B A (2 cases) In Circular: A B or B A, but same relative position

Pattern 2: Between

“Exactly 2 people between A and B”

In Linear (5 positions): A _ _ B or B _ _ A (positions 1 and 4, or 2 and 5)

In Circular (6 positions): If A at 1, B at 4 (1 → 2 → 3 → 4, positions 2, 3 between)

Pattern 3: Not Adjacent

“A and B do not sit together”

Eliminate cases where A and B are immediate neighbors

Pattern 4: Extreme Ends

Linear: Positions 1 and N (leftmost and rightmost)

“A sits at one extreme” = A at 1 or N (2 cases) “A does not sit at extreme” = A at 2 to (N-1)

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🎯 Advanced Patterns

Multi-Variable Puzzles

Example Pattern:

7 people with 3 attributes each:

• Name (A, B, C, D, E, F, G)
• Profession (Doctor, Engineer, Lawyer, etc.)
• City (Delhi, Mumbai, Kolkata, etc.)

Match all three for each person.

Strategy:

1. Create a table with rows = people, columns = attributes
2. Mark definite matches with ✓
3. Mark definite non-matches with ✗
4. Use elimination

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Comparison-Based Puzzles

Example:

5 people with different heights, weights, ages

Conditions like:

• A is taller than B but shorter than C
• D is heavier than E
• etc.

Create comparison chains: C > A > B

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📝 Practice Problems

Level 1: Linear Arrangement

1. Five people P, Q, R, S, T sit in a row facing North.

• P sits at one extreme
• R sits second from left
• S sits between Q and T

Find the arrangement.

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Level 2: Circular Arrangement

2. Six people A, B, C, D, E, F sit around a circular table facing center.

• A sits opposite to D
• B sits second to the right of A
• C is not adjacent to A
• E sits between C and F

Find the arrangement.

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Level 3: Floor-Based

3. Seven people live on 7 different floors (1-7).

• A lives on 3rd floor
• Three floors between A and B
• C lives immediately below B
• D lives on an even-numbered floor
• E lives above F but below G

Find who lives on each floor.

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🔗 Related Topics

Uses Concepts From:

• Blood Relations - Relationship mapping
• Direction Sense - Left/right/facing

Related Reasoning Topics:

• Syllogism - Logical deduction
• Data arrangement problems

Practice:

• Puzzles & Seating Arrangement Questions

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Master Puzzles - Draw diagrams, use definite conditions first! 🧩