Circular and square seating for IBPS PO

Circular seating is the puzzle type most aspirants think they know, until a set mixes people facing the centre with people facing outside. Then "second to the right" means one thing for one person and the opposite for the next, and a single slip ruins five questions.

The fix is mechanical: number the seats, and turn every clue into seat arithmetic before you place anyone. Below are the rule, the method, two PO-level worked sets and a square-table practice set.

Left and right in a circle

Draw the circle and number the seats 1 to 8 clockwise, as seen from above. Now picture yourself sitting at the bottom of the circle, facing the centre. Your right hand points to the seat that is anticlockwise from you. Turn round to face outside and your right hand points clockwise.

Wrap round the circle: with 8 seats, seat 8 + 1 is seat 1, and seat 1 − 1 is seat 8.

Three clues never depend on facing, so they are your anchors:

• Opposite: with 8 seats, seat n faces seat n + 4.
• Immediate neighbours: seats n − 1 and n + 1.
• "Only two people sit between X and Y": count along the shorter side, so X and Y are three seats apart. The other side then has four people between them.

The method

1. Draw eight seats and number them clockwise. Put the first person you are sure of at seat 1. In a circle, any seat can be seat 1.
2. Place everything that the facing-free clues fix: opposite, neighbours, "between".
3. For each facing clue, write the seat arithmetic in the margin: "B = A − 3" if A faces the centre.
4. When a clue gives two positions, draw two small circles, Case 1 and Case 2.
5. When a person's facing is unknown, try both facings. The seats already taken usually kill one.
6. Check every clue against the finished circle before you answer.

Worked set 1: everyone faces the centre, with colours

Eight friends, P, Q, R, S, T, U, V and W, sit around a circular table facing the centre. Each likes a different colour: Black, Blue, Green, Grey, Pink, Red, White and Yellow.

1. P sits third to the left of S.
2. U sits opposite S.
3. Q sits immediately to the right of P.
4. Only one person sits between T and U.
5. W sits immediately to the left of T.
6. V is not an immediate neighbour of U.
7. The person who likes Red sits second to the right of P.
8. The person who likes Blue sits opposite the person who likes Black.
9. The person who likes Green sits second to the left of the person who likes Blue.
10. The person who likes Pink sits immediately to the right of R.
11. The person who likes White sits opposite W.
12. W does not like Yellow.

Placing the people

Everyone faces the centre, so left is + (clockwise) and right is − (anticlockwise).

• Put S at seat 1. Clue 1: P = 1 + 3 = 4. Clue 2: U = 5.
• Clue 3: Q = P − 1 = 3.
• Clue 4: T is two seats from U, so seat 3 or 7. Seat 3 is Q's, so T = 7. Clue 5: W = 7 + 1 = 8.
• Seats 2 and 6 remain for R and V. Seat 6 is next to U, so clue 6 gives V = 2 and R = 6.

Placing the colours

• Clue 7: Red = P − 2 = seat 2, so V likes Red.
• Clue 11: White is opposite W (seat 8), at seat 4, so P likes White.
• Clue 10: Pink = R − 1 = seat 5, so U likes Pink.
• Clue 8: Blue and Black are opposite each other. The free seats are 1, 3, 6, 7 and 8, and the only opposite pair among them is 3 and 7.
  • If Q (seat 3) liked Blue, Green would be at seat 5, which is U's (Pink). So T likes Blue and Q likes Black.
  • Clue 9: Green = 7 + 2 = seat 9, which wraps to seat 1, so S likes Green.
• Clue 12: W likes Grey, and R likes Yellow.

Questions

1. Who likes Yellow? R.
2. Who sits second to the right of U? Q. U is at seat 5; right is −, so seat 3.
3. Who sits opposite the person who likes Red? R. V is at seat 2; opposite is seat 6.
4. How many people sit between P and T, counting from P's left? Two (U and R). P's left is clockwise: seats 5 and 6, then T.
5. Who sits immediately to the left of the person who likes Grey? S. W is at seat 8; left is +, so seat 1.

Worked set 2: mixed facing

Eight people, A, B, C, D, E, F, G and H, sit around a circular table. Some face the centre and some face outside.

1. A faces the centre. E sits opposite A and faces the same direction as A.
2. B sits third to the right of A.
3. C sits second to the right of E.
4. D is an immediate neighbour of A, and D faces outside.
5. G sits immediately to the left of D.
6. H sits immediately to the left of C.
7. Both immediate neighbours of H face the direction opposite to H.
8. F and G face the same direction.
9. Exactly four people face the centre.

Solving

• A = 1, facing the centre. Clue 1: E = 5, facing the centre.
• Clue 2: A's right is −, so B = 1 − 3 = −2, which wraps to seat 6.
• Clue 3: E's right is −, so C = 3.
• Clue 4: D is at seat 2 or 8. D faces outside, so D's left is − (anticlockwise). If D = 2, G = 1, which is A's seat. So D = 8 and G = 7.
• Clue 6: C's facing is unknown, so try both. Facing the centre, C's left is seat 4. Facing outside, it is seat 2. Both are free, so check clue 7.
  • If H = 2, H's neighbours are A (centre) and C (outside). They face different ways, so they cannot both be opposite to H. This case fails.
  • So H = 4 and C faces the centre. H's neighbours C and E both face the centre, so H faces outside.
• F takes seat 2.
• Facings so far: A, E and C face the centre; D and H face outside. Clue 9 needs one more person facing the centre among B, F and G. Clue 8 says F and G match, so both face outside and B faces the centre.

Questions

1. How many people face outside? Four (F, H, G and D).
2. Who sits second to the left of B? D. B faces the centre, so left is +: seats 7, 8.
3. Who sits immediately to the right of F? C. F faces outside, so right is +: seat 3.
4. Who sits third to the left of H? A. H faces outside, so left is −: seats 3, 2, 1.
5. Which two people facing outside sit next to each other? G and D.

Square and rectangular tables

A square table with eight people usually has four at the corners and four at the middles of the sides. Treat it as a circle of eight seats numbered clockwise from a corner, so corners are seats 1, 3, 5 and 7. The facing rules are the same as for a circle. The only new clues are "sits at a corner" and "sits in the middle of a side", which tell you whether a seat number is odd or even.

A common twist: people at the corners face the centre and people at the middles face outside. Then every seat has a fixed facing, and you can apply the rule seat by seat.

Common mistakes

• Using clockwise for "right" when a person faces the centre, or judging by the placed person's facing instead of the reference person's.
• Forgetting to wrap round past seat 8 or below seat 1.
• Reading "only two people between" as one fixed position. It gives two seats, one on each side.
• Answering before every facing is fixed. A question about "second to the left" is wrong if the facing is still a guess.

Practice set: a square table

Eight people, J, K, L, M, N, O, Y and Z, sit around a square table. Four sit at the corners and face the centre. Four sit in the middles of the sides and face outside.

1. J sits at a corner. K sits opposite J.
2. L sits second to the left of J.
3. N sits immediately to the right of L.
4. M sits immediately to the right of J.
5. Z sits second to the left of M.
6. O sits at a corner.

Questions

1. Who sits opposite N?
2. Who sits immediately to the right of Y?
3. Who sits second to the left of K?
4. Who sits immediately to the left of O?
5. Who is an immediate neighbour of both L and K?
6. Who is an immediate neighbour of both M and N?

Solution

Number the seats clockwise from J's corner, so J = 1 and the corners are 1, 3, 5 and 7. K = 5. J faces the centre, so left is +: L = 3. L faces the centre, so right is −: N = 2. M = J − 1 = 8. M sits in a middle and faces outside, so left is −: Z = 6. The only corner left is 7, so O = 7. Y takes seat 4.

Answers

1. Z. N is at seat 2; opposite is seat 6.
2. K. Y faces outside, so right is +: seat 5.
3. O. K faces the centre, so left is +: seats 6, 7.
4. M. O faces the centre, so left is +: seat 8.
5. Y (seat 4).
6. J (seat 1, between seats 8 and 2), a corner seat.

What to do next

• Redo worked set 2 from the clues alone, writing the seat arithmetic ("B = A − 3") beside each clue.
• Solve one circular set a day for two weeks, alternating all-centre and mixed facing.
• Revise linear seating for the row version of the same rule, and floor and box puzzles for case building.