Seating Arrangements Concepts

1. Circular Table Puzzles

How It Works

People sit in a circle around a table, and their left/right orientation depends on which way they are facing:

• Facing the Center: Clockwise = Left | Anticlockwise = Right
• Facing Outward: Clockwise = Right | Anticlockwise = Left

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Example Problem

Six friends (A, B, C, D, E, F) sit around a circular table facing the center.

• A is opposite D.
• B is second to the left of A.
• C is to the immediate right of B.
• E is between D and F.

Find the clockwise seating order starting from A.

                 A (1)
           F (6)     E (2)

         B (5)         D (4)

                C (3)

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Step-by-Step Solution

1. Place A: Put A at the top (position 1). Number the seats 1 to 6 clockwise.
2. Place D: Because A is opposite D in a group of 6, D is 3 seats away.

• Position = $1 + 3 = 4$. Place D at position 4.

3. Place B: B is second to the left of A.

• Since they face the center, “left” means clockwise. Moving 2 spots clockwise from A lands on position 6. Place B at position 6.

4. Place C: C is to the immediate right of B.

• “Right” means anticlockwise. Moving 1 spot anticlockwise from B (position 6) leads to position 5. Place C at position 5.

5. Place E and F: E is between D (position 4) and F.

• The only remaining empty spots are 2 and 3. Since E is between D and F, F goes to position 3 and E goes to position 2.

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Final Answer

Clockwise order starting from A: A, E, F, D, C, B

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2. Square & Rectangular Table Puzzles

How It Works

People sit at tables with corners and sides.

• Corners: People at corners face diagonally across from them.
• Sides: People in the middle of a side face the person directly across from them.

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Example Problem

Eight people sit at a rectangular table with 2 people on each long side and 1 person on each short side.

• P sits at a corner.
• Q sits diagonally opposite P.
• R sits on the same side as P, but not at a corner.
• S sits opposite R.
• T sits between P and R.

Find the complete seating arrangement.

           Long Side

      P ----- T ----- R
      |               |
   V  |               |  W
      |               |
      Q ----- U ----- S

           Long Side

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Step-by-Step Solution

1. Place P: Set P at the corner of Long Side 1.
2. Place R and T: R is on the same side as P (not a corner), and T is between them.

• This means Long Side 1 contains: P (corner) $\rightarrow$ T (middle) $\rightarrow$ R (corner).

3. Place Q: Q is diagonally opposite P.

• Since P is at a corner on Long Side 1, Q must be at the opposite corner on Long Side 2.

4. Place S: S sits opposite R.

• Since R is at a corner, S sits directly across at the corner on Long Side 2.

5. Fill the rest: Place the remaining people on the short sides and middle spots.

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Final Answer

• Long Side 1: P, T, R
• Short Side 1: V
• Long Side 2: Q, U, S
• Short Side 2: W

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3. Polygon Seating (Hexagon / Octagon)

How It Works

Similar to circular tables, but with straight edges (e.g., a hexagon has 6 fixed seats).

• Clues like “three places away” mean you skip 2 people in between.
• Opposites are calculated by splitting the total number of seats in half.

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Example Problem

Six people (A, B, C, D, E, F) sit at a hexagonal table.

• A is at position 1.
• B is two seats away clockwise from A.
• C faces A (is directly opposite).
• D is between B and C.

Find all positions.

          (1) A

     (6) F     E (2)

     (5) D     B (3)

          (4) C

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Step-by-Step Solution

1. Place A: Set A at position 1.
2. Place B: B is two seats away clockwise (skip 1 person).

• $1 + 2 = 3$. Place B at position 3.

3. Place C: C faces A (3 seats away in a 6-person shape).

• $1 + 3 = 4$. Place C at position 4.

4. Place D: D is between B (position 3) and C (position 4).

• Since 3 and 4 are right next to each other, D must sit on the longer path around the hexagon connecting them, which is position 5.

5. Place E and F: The remaining empty seats (2 and 6) go to E and F.

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Final Answer

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

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4. Hybrid Scheduling (People + Attributes)

How It Works

These puzzles combine seating arrangements with extra details (like cities, jobs, or colors). Use a step-by-step elimination method to match each person to their specific traits.

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Example Problem

Five people (A, B, C, D, E) sit in a row facing North. They have different cities (Delhi, Mumbai, Kolkata, Chennai, Bengaluru) and jobs (Doctor, Engineer, Teacher, Artist, Pilot).

• The Doctor sits in the middle (position 3).
• A is from Mumbai.
• The Engineer sits at the extreme right (position 5).
• The Teacher is from Kolkata.
• B is the Pilot and sits right next to A.
• C sits to the left of D.
• The person from Chennai sits between the Artist and the Doctor.

Find each person’s city and profession.

North

A        B        E        C        D
1        2        3        4        5

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Step-by-Step Solution

1. Fix Known Positions:

• Position 3 = Doctor
• Position 5 = Engineer

2. Use Clues for A and B:

• B is the Pilot and sits next to A.
• If A is placed at position 1, B must be at position 2 (Pilot).

3. Place the Artist and Chennai:

• The Chennai person is between the Artist and the Doctor (position 3).
• Since Doctor is at 3, Chennai must be at position 2, and the Artist must be at position 1.
• Result so far: A (Position 1) = Artist from Mumbai. B (Position 2) = Pilot from Chennai.

4. Place Teacher and Engineer:

• The Engineer is at position 5.
• The Teacher is from Kolkata. C sits to the left of D.
• This leaves position 4 for the Teacher (from Kolkata) and position 5 for the Engineer (from Bengaluru).

5. Assign the Last Person:

• E takes the remaining middle spot as the Doctor from Delhi.

Final Answer

• A: Artist | Mumbai
• B: Pilot | Chennai
• C: Teacher | Kolkata
• D: Engineer | Bengaluru
• E: Doctor | Delhi