Geometrical Seating Arrangement: Square, Rectangular and Triangular Table Puzzles with Solved Examples for SSC

In a geometrical seating arrangement, people sit around a square, rectangular or triangular table, some at the corners and some at the middle of the sides, and they may face the centre or face outside. The key to these puzzles is the left and right rule, which changes with the direction of facing. This guide on geometrical seating arrangement for SSC explains the rule, the method and a complete solved puzzle with practice questions.

Types of Geometrical Arrangements

The Left and Right Rule

Number the seats clockwise (1, 2, 3, …). The following rule works for any shape:

This rule is the reverse for people facing the centre and people facing outside. Many wrong answers come from forgetting this reversal.

Opposite Seats

For 8 persons around a square table, the person opposite to the person in seat k is in seat k + 4 (or k − 4). The persons in the corners are opposite other corner persons, and the persons at the middle of the sides are opposite other middle persons.

Method to Solve

1. Draw the shape and number the seats clockwise.
2. Mark which seats are corners and which are at the middle of sides, and which direction they face.
3. Place the definite statements first (those that give a direct position).
4. Use the left and right rule to place others, and use “opposite” as seat + 4 (for 8 seats).
5. Fill the remaining persons in the empty seats and check all statements.

Solved Puzzle

Eight friends P, Q, R, S, T, U, V and W sit around a square table. Four of them sit at the corners and face the centre, and the four others sit at the middle of the sides and face outside. Seats are numbered 1 to 8 clockwise, with seat 1 at a corner (so odd seats are corners and even seats are the middle of sides).

• P sits at a corner (seat 1).
• Q sits to the immediate right of P.
• R sits opposite Q.
• S sits to the immediate left of R.
• T sits between P and S.
• U sits at the corner opposite P.
• V sits to the immediate left of U.
• W sits in the remaining seat.

Solution. P is at seat 1 and faces the centre, so P’s right is the anticlockwise neighbour: Q is at seat 8. R is opposite Q, so R is at seat 4. R faces outside, so R’s left is the anticlockwise neighbour: S is at seat 3. T sits between P (1) and S (3), so T is at seat 2. U is opposite P, so U is at seat 5. U faces the centre, so U’s left is the clockwise neighbour: V is at seat 6. W takes seat 7.

Questions on this Puzzle

Who sits opposite T? Seat 2 + 4 = seat 6, which is V.

Who sits to the immediate right of S? S is at seat 3 and faces the centre, so the right is the anticlockwise seat 2: T.

Who sits second to the left of W? W is at seat 7 and faces the centre, so the left is clockwise: seat 8 (Q), then seat 1 (P). The answer is P.

Tricks

• Always write the facing direction of each seat before using left or right.
• Put the persons who are fixed by direct statements first.
• Use seat numbers and the +4 rule for opposite persons in 8-seat tables.
• In rectangular tables, persons on the longer sides face each other, and those on the shorter sides face the centre or outside as stated.
• After placing all persons, test every statement again.

Quick Tips

• Number the seats clockwise.
• Reverse left and right for persons facing outside.
• Use +4 for opposite seats in an 8-person table.
• Re-check every statement after placing all persons.

Quick Revision Points

• Facing the centre: left is clockwise and right is anticlockwise.
• Facing outside: left is anticlockwise and right is clockwise.
• Opposite seat in an 8-seat table = seat + 4.
• Corners and side-middles often face different directions.
• Fix definite statements first.

Practice Questions With Answers

1. In the solved puzzle, who sits opposite T?
   Answer: V
2. Who sits to the immediate right of R?
   Answer: U
3. Who sits between W and P?
   Answer: Q
4. Who sits second to the left of Q?
   Answer: V
5. Which persons sit at the corners?
   Answer: P, S, U and W
6. Who sits opposite R?
   Answer: Q
7. How many persons sit between U and Q (going clockwise from U)?
   Answer: 2 (V and W)
8. Who sits to the immediate left of T?
   Answer: P
9. Who sits third to the right of S?
   Answer: Q
10. Who sits opposite W?
    Answer: S

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Reasoning notes page, read the previous topic Cube Cutting and Painting.

Frequently Asked Questions

What is a geometrical seating arrangement?

It is a puzzle in which people sit at the corners and sides of a square, rectangle or triangle and face the centre or outside.

How does left and right change when facing outside?

The left and right are reversed compared with a person facing the centre.

If a person faces the centre, who is on the immediate left?

The clockwise neighbour.

How do I find the opposite person in an 8-seat table?

Add or subtract 4 from the seat number.

How do I begin solving such puzzles?

Draw the shape, number the seats and place the persons given by direct statements.

What is the usual arrangement in a square table with 8 persons?

Four at the corners and four at the middle of the sides.

How are rectangular tables different?

The persons on the longer sides face each other, and the shorter sides have fewer persons.

What if some persons face the centre and some face outside?

Apply the left and right rule separately for each person.

Is this topic asked in SSC?

Yes, seating arrangement puzzles appear in SSC CGL, CHSL and other reasoning papers.

How much time should a set take?

About 3 to 4 minutes for 5 questions.

Can I draw a table on paper?

Yes. A rough diagram saves a lot of time and prevents mistakes.

What are common mistakes?

Forgetting to reverse left and right, and placing persons without checking all statements.