Circular seating for SBI PO

Circular seating puts people around a round table, usually equally spaced. It has two features a straight row does not. There is no first seat, so you must choose a starting point yourself. And "left" and "right" become "clockwise" and "anticlockwise", which flip depending on whether a person faces the centre or faces outside. Mains puzzles use both features, often with a mix of inward- and outward-facing people.

Get the direction rule right and fix one person before you place anyone else. The rest is the same case-building you use for floors and rows.

The direction rule

Why. Imagine sitting at the table facing the centre. Your left hand points along the edge of the table in the clockwise direction. Turn round to face outside and your hands swap: now your left points anticlockwise.

Useful counts

"Only one person sits between A and B" means B is two seats from A. On a round table there are two ways round, so the clue usually allows two seats. That is a natural place to branch.

The case-building method

1. Draw the circle and number the seats clockwise.
2. Fix a reference. Put the person named in the most definite clue at seat 1.
3. Place people relative to that person, checking each one's facing before you use left or right.
4. Branch when a clue allows two seats, and draw two small circles side by side.
5. Test each new clue on every open case, and cross out a case as soon as it breaks.
6. For mixed facing, mark an arrow (in or out) at each seat as soon as it is known.
7. Check every clue against the final circle before answering.

An SBI PO-level puzzle: eight people facing the centre

Eight people, P, Q, R, S, T, U, V and W, sit around a circular table, equally spaced, all facing the centre.

1. P sits second to the left of T.
2. V sits immediately to the right of T.
3. Only one person sits between R and V.
4. S sits opposite R.
5. U sits immediately to the left of P.
6. W sits immediately to the right of S.

Step 1: fix T. Put T at seat 1 and number the seats 1 to 8 clockwise. Everyone faces the centre, so left is clockwise and right is anticlockwise.

• P is two seats clockwise from T: seat 3.
• V is one seat anticlockwise from T: seat 8.
• U is one seat clockwise from P: seat 4.

Step 2: branch on R. Only one person sits between R and V (seat 8). R is two seats from V, either way: seat 2 or seat 6.

S sits opposite R, four seats away, so S is at 6 in Case 1 and at 2 in Case 2.

Step 3: test clue 6. W sits immediately to the right of S, one seat anticlockwise.

• Case 1: S at 6, so W at 5. Free. The last seat, 7, goes to Q.
• Case 2: S at 2, so W at 1. T is at 1. Case 2 fails.

Every other seating (with T fixed at seat 1) breaks at least one clue, so this is the only solution.

Questions:

1. Who sits opposite T?
2. Who sits third to the left of V?
3. How many people sit between U and V, counting clockwise from U?
4. Who sits immediately to the right of Q?
5. Who sits opposite U?

Answers:

1. W (seat 5).
2. P. Left is clockwise: from seat 8, three seats on is seat 3.
3. Three: W, S and Q.
4. S. Right is anticlockwise: from seat 7 to seat 6.
5. V (seat 8).

Mixed facing: some in, some out

Mains puzzles often say "some face the centre and some face outside". The rule table above still works; you just have to apply it person by person. Two habits help:

• Draw an arrow at each seat (pointing in or out) the moment a clue fixes it.
• Use left and right clues to work out direction. If you know both people's seats, a clue like "D sits immediately to the right of B" tells you which way B faces.

Other variations

• Square or rectangular tables. Some people sit at the corners and some at the middles of the sides. The same clockwise rule applies. Draw the shape and number seats clockwise from one corner.
• A second variable. Professions or favourite colours. Write them outside the circle next to each seat.
• Seven people. No one sits directly opposite anyone, so clues count the people between instead. Each such clue allows two seats, one each way round, so branch early.

Common mistakes

• Using the page's left and right instead of the seated person's.
• Forgetting to flip the rule for someone facing outside.
• Treating "between" as one-way on a circle. Always check both ways round.
• Placing people before fixing a reference seat, which leaves you with a diagram that slides around the table.

Practice puzzle: mixed facing

Six people, A, B, C, D, E and F, sit around a circular table, equally spaced. Some face the centre and some face outside.

1. A faces the centre, and B sits second to the left of A.
2. D is an immediate neighbour of both A and B.
3. C sits opposite D and faces the centre.
4. F sits immediately to the right of C.
5. D sits immediately to the right of B.
6. E sits second to the left of F.
7. Both immediate neighbours of E face the opposite direction to E.
8. D faces the opposite direction to the person who sits opposite D.

Questions:

1. How many people face the centre?
2. Who sits immediately to the left of D?
3. Who sits opposite B?
4. Who sits second to the right of E?

Answers (A at seat 1, seats numbered clockwise):

1. Four: A, B, C and F. A faces in, so B is two seats clockwise, at 3. D sits between them, at 2. C is opposite D at 5 and faces in, so F is one seat anticlockwise, at 4. E takes 6. D is anticlockwise of B, which is B's right only if B faces in. E is two seats clockwise of F, which is F's left only if F faces in. E's neighbours, A and C, both face in, so E faces out. The person opposite D is C, who faces in, so D faces out.
2. A. D faces outside, so D's left is anticlockwise: seat 1.
3. E. Three seats from seat 3 is seat 6.
4. D. E faces outside, so E's right is clockwise: from seat 6, two seats on is seat 2.

Final circle, clockwise from seat 1: A (in), D (out), B (in), F (in), C (in), E (out).

What to do next

• Redo the eight-person puzzle from a blank circle, in under 6 minutes.
• Solve two mixed-facing puzzles a day for a week, marking arrows first.
• Revise linear seating for the north–south version of the same rule, and check the reasoning plan for how much seating practice to schedule.