Linear seating for SBI PO

Linear seating puts people in a straight row and asks who sits where. In the prelims everyone usually faces the same way. In the mains, people often face different directions, and that single change is what turns a four-minute set into a ten-minute one. Every clue with "left" or "right" now depends on which way the person in the clue is facing.

The fix is mechanical. Draw an arrow over every seat the moment you know it, and read each "left" or "right" from the seated person's point of view, never your own.

Direction rules

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

A quick check: stand up and face north. Your right hand points east, which is the right of the page. Turn to face south and your right hand points west, the left of the page.

Key phrases

The case-building method

1. Draw the seats with numbers, and leave space above each for an arrow.
2. Place definite clues and draw each person's arrow as soon as it is known.
3. Branch on the first clue with two options (for example "at one of the extreme ends"). Draw both rows.
4. Test each new clue on every open row. For every "left" or "right", look at the arrow first.
5. Settle directions last. Clues such as "exactly four people face north" usually decide the leftover arrows.
6. Check every clue against the final row, arrows included.

An SBI PO-level puzzle: eight people, mixed directions

Eight people, A, B, C, D, E, F, G and H, sit in a row. Some face north and some face south.

1. D sits at one of the extreme ends and faces south.
2. Only three people sit between A and D.
3. A faces north, and H sits immediately to the right of A.
4. H faces the opposite direction to A.
5. C sits immediately to the left of H and faces north.
6. F sits immediately to the right of C.
7. G sits second to the left of A.
8. B sits at one of the extreme ends.
9. The two people at the extreme ends face opposite directions.
10. E and G face opposite directions, and E and F face the same direction.
11. Exactly four people face north.

Step 1: branch on D and A. D is at seat 1 or 8. With three people between them, A is four seats away from D.

• Case 1: D at 1, A at 5.
• Case 2: D at 8, A at 4.

Step 2: H, C, F and G in each case. A faces north, so A's right is the higher seat: H is at A + 1 and faces south. H faces south, so H's left is the higher seat: C is at H + 1. C faces north, so F is at C + 1. G is two seats to A's left, at A − 2.

Count every "second to the left" on the diagram, seat by seat, not in your head. It is the easiest place to slip by one.

Step 3: test clue 8. B sits at an end. In Case 1 both ends are taken, by D and F. Case 1 fails. In Case 2, B is at seat 1, and the only seat left, 3, goes to E.

Step 4: directions. So far: A and C face north; D and H face south.

• The two ends, B and D, face opposite directions (clue 9), so B faces north. That makes three people facing north.
• E, F and G are left. E and F face the same way, and G the other way (clue 10). Exactly four face north (clue 11), so only one of the three can face north. That must be G alone, because E and F go together.
• So G faces north; E and F face south.

This is the only arrangement, seats and directions together, that fits all eleven clues; every other combination was tested and fails.

Questions:

1. Who sits second to the right of G?
2. Who sits immediately to the left of F?
3. Who sits immediately to the right of E?
4. How many people sit between B and C?
5. How many people face south?

Answers:

1. A. G faces north, so right means higher seats: seat 4.
2. D. F faces south, so F's left is the higher seat: seat 8.
3. G. E faces south, so E's right is the lower seat: seat 2.
4. Four: G, E, A and H.
5. Four: E, H, F and D.

Other mains variations

• Unknown number of people. "Some people sit in a row." Place the named people first and count the unnamed seats from clues such as "three people sit between A and B".
• Two parallel rows facing each other. One row faces north, the other south. "Faces A" means directly opposite A. Draw both rows with seat numbers matching across the gap.
• A second variable. Professions or favourite items. Add a row of labels under the seats.

Practice puzzle

Seven people, J, K, L, M, N, O and P, sit in a row facing north.

1. J sits third from one of the ends.
2. Only one person sits between J and O, and O sits to the right of J.
3. L sits immediately to the right of O.
4. M sits immediately to the left of O.
5. K sits second to the left of J.
6. N does not sit at an extreme end.

Questions:

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

Answers (seats 1 to 7 from the left):

1. P. J is at 3 or 5. If J were at 5, O would be at 7 and L at 8, which does not exist. So J is at 3, O at 5, L at 6, M at 4 and K at 1. N cannot be at an end, so N takes 2 and P takes 7.
2. Three: N, J and M.
3. L.
4. N.

Final row: K, N, J, M, O, L, P.

What to do next

• Redo the eight-person puzzle from a blank page, drawing arrows first, in under 7 minutes.
• Solve two mixed-direction puzzles a day for a week.
• Move on to circular seating, where left and right become clockwise and anticlockwise, and see the reasoning plan.