🧩 Puzzles & Seating Arrangement - Complete Theory

Master arrangement problems - highest weightage in IBPS Reasoning!

🎯 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

📐 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

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

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)

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

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

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

🎯 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.

💡 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

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

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)

⚡ 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.

⚠️ 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.

📊 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)

🎯 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

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

📝 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.

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.

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.

🔗 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

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