Linear seating arrangement for IBPS PO

Linear seating is where most careless errors in IBPS PO reasoning happen, and nearly all of them come from one source: taking left and right from your own view instead of from the person's. Fix that habit and linear seating becomes one of the more reliable sources of marks.

The puzzles come in three forms. Everyone faces north (the easy form). Everyone faces south (the same puzzle mirrored). Or some face north and some face south, where each person's left and right must be worked out separately. PO-level sets often add a second variable, such as a city or a subject.

Left and right, once and for all

Draw the row across your page with north at the top of the page. Number the seats 1, 2, 3… from the left of the page.

Why: if you face north, your right hand points east, which is the right of a normal map. Turn around to face south, and your right hand now points west, the left of the map.

"Only two people between X and Y" and "X sits at an extreme end" do not depend on anyone's facing. They are your anchors when the facings are still unknown.

The case-building method

1. Draw the seats and number them from the left of the page.
2. Start with clues that do not depend on facing: ends, "between", "fourth from the end".
3. When a clue allows two positions, write Case 1 and Case 2 as two rows, one under the other.
4. For facing-dependent clues, try both facings if the person's direction is unknown. Often only one fits the row, and that also tells you the facing.
5. Kill a case the moment a clue fails. Check every clue at the end.

Worked set 1: mixed facing

Eight people, A, B, C, D, E, F, G and H, sit in a row. Some face north and some face south. Seats are numbered 1 to 8 from the left of the page.

1. E sits at one of the extreme ends of the row. Only two people sit between E and D.
2. D faces south. G sits immediately to the right of D.
3. B sits second to the right of D.
4. F sits at one of the extreme ends.
5. A sits third to the right of F.
6. A faces north. H sits immediately to the right of A.
7. Both immediate neighbours of G face the direction opposite to G.
8. C faces the same direction as F.
9. The two people at the extreme ends face opposite directions.
10. H faces the same direction as A.

Building the cases

• Clue 1: Case 1: E = 1, D = 4 or Case 2: E = 8, D = 5.
• Clue 2: D faces south, so D's right is the page's left. Case 1: G = 3. Case 2: G = 4.
• Clue 3: B is two seats to D's right. Case 1: B = 2. Case 2: B = 3.
• Clue 4: F takes the other end. Case 1: F = 8. Case 2: F = 1.
• Clue 5: A is three seats to F's right, and F's facing is unknown, so try both.
  • Case 2 (F = 1): facing north puts A at seat 4, which is G's; facing south puts A off the row. Case 2 fails.
  • Case 1 (F = 8): facing north puts A off the row, so F faces south and A = 5.

Finishing Case 1

• Clue 6: A faces north, so H is at seat 6. C takes seat 7.
• Clue 7: G's neighbours are B (seat 2) and D (seat 4). D faces south, so G faces north and B faces south.
• Clue 8: C faces south, like F.
• Clue 9: F (seat 8) faces south, so E (seat 1) faces north.
• Clue 10: H faces north.

Questions

1. How many people face north? Four (E, G, A and H).
2. Who sits second to the left of G? E. G faces north, so left is the page's left: seat 1.
3. Who sits immediately to the right of C? H. C faces south, so right is the page's left: seat 6.
4. How many people sit between B and H? Three (G, D and A).
5. Who sit at the two extreme ends? E and F.

Worked set 2: one direction, two variables

Seven people, P, Q, R, S, T, U and V, sit in a row facing north. Each is from a different city: Agra, Bhopal, Delhi, Kochi, Patna, Pune and Surat.

1. R sits third from one of the ends of the row.
2. Only one person sits between R and T. T does not sit at an end.
3. P sits immediately to the right of T. P is from Surat.
4. P sits second to the left of Q.
5. Q is from Pune. T is from Agra.
6. Only four people sit between U and V. U sits to the right of V.
7. The person from Delhi sits immediately to the right of the person from Kochi.
8. R is not from Patna.

Building the cases

• Clue 1: Case 1: R = 3 or Case 2: R = 5.
• Clue 2: T is two seats from R and not at an end. Case 1: T = 1 or 5, so T = 5. Case 2: T = 3 or 7, so T = 3.
• Clue 3: P is at T + 1. Case 1: P = 6. Case 2: P = 4.
• Clue 4: Q is at P + 2. Case 1: Q = 8, which does not exist. Case 1 fails. Case 2: Q = 6.

Finishing Case 2

• Seats 1, 2 and 7 remain for S, U and V. Clue 6: U and V are five seats apart with U on the right, so V = 2 and U = 7. S = 1.
• Cities so far: P Surat, Q Pune, T Agra. Kochi, Delhi, Bhopal and Patna remain for seats 1, 2, 5 and 7.
• Clue 7: Kochi and Delhi must be adjacent, and the only adjacent free pair is seats 1 and 2. So S is from Kochi and V from Delhi.
• Clue 8: R is from Bhopal, and U is from Patna.

Questions

1. Who is from Delhi? V.
2. How many people sit to the right of T? Four (P, R, Q and U).
3. Who sits exactly in the middle of the row? P, from Surat.
4. Who sits second to the right of R? U, from Patna.
5. Who sit at the two extreme ends? S and U.

Common mistakes

• Taking left and right from your own view for a south-facing person.
• Using the placed person's facing instead of the reference person's. In "G sits to the right of D", D's facing decides.
• Assuming "between" gives a direction. It gives two cases.
• Forgetting the end of the row. "Third to the right" from seat 7 of 8 does not exist, and that often kills a case.
• Answering facing questions before every facing is fixed. Finish the table first.

Practice set

Six people, J, K, L, M, N and O, sit in a row. All of them face south. Seats are numbered 1 to 6 from the left of the page.

1. L sits at one of the extreme ends.
2. Only three people sit between L and N.
3. O sits immediately to the right of L.
4. J sits second to the right of O.
5. M sits immediately to the left of J.

Questions

1. Who sits immediately to the right of N?
2. Who sits second to the left of N?
3. How many people sit between K and O?
4. Who sits immediately to the left of M?

Answers

Everyone faces south, so right is the page's left. O is immediately right of L, so O is at L's seat − 1. That rules out L = 1, so L = 6 and O = 5. N is four seats from L, so N = 2. J is two seats to O's right: seat 3. M is immediately to J's left, which is the page's right: seat 4. K takes seat 1.

1. K (seat 1).
2. M (seat 4).
3. Three (N, J and M).
4. O (seat 5).

What to do next

• Redo worked set 1 from the clues alone, saying "D's right is the page's left" out loud at each step.
• Solve two linear seating sets a day for a week, one of them with mixed facing.
• Move on to circular seating, where the same rule applies to facing the centre and facing outside, and revise floor and box puzzles for the case method.