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Linear Seating Arrangement Tricks: Fixed Clues First, North and South Facing

Number the seats • Fixed clues before relative clues • Branch and eliminate • Facing south flips left and right • Position from both ends

Banking SSC 📅 Last updated: 2026-10-23

A linear seating puzzle puts a group of people in a single row and gives a list of clues about who sits where. Six people can sit in a row in 6! = 720 ways, so trying arrangements at random is hopeless. The clues have to be used in an order that cuts down the possibilities quickly.

Clues come in two kinds. A fixed clue names a seat directly, such as "C sits third from the left end" or "A sits at an extreme end". A relative clue only links two people, such as "E sits immediately to the right of C". Fixed clues go first, because they pin people to seats. Relative clues are then placed against those people.

Draw the row and number the seats 1, 2, 3 and so on from left to right, as seen by a person facing north. Then every clue becomes arithmetic on seat numbers:

Clue for a person facing northSeat arithmetic
X is immediately right of YX = Y + 1
X is second to the left of YX = Y − 2
One person sits between X and Ythe seats differ by 2
X is at an extreme endX is seat 1 or the last seat
X and Y are neighboursthe seats differ by 1

In a row of 6, "third from the right end" is seat 6 − 3 + 1 = 4.

Worked example 1: six people in a row

A, B, C, D, E and F sit in a row facing north.

  1. C sits third from the left end.
  2. Only one person sits between A and C.
  3. A sits at an extreme end.
  4. E sits immediately to the right of C.
  5. B sits next to D.
  6. B does not sit at an end.

Solution. Clue 1 is fixed: C is in seat 3. Clue 2 puts A in seat 1 or seat 5, and clue 3 picks seat 1. Clue 4 puts E in seat 4. Seats 2, 5 and 6 remain for B, D and F. B's neighbours in seat 2 would be A and C, so clue 5 rules seat 2 out for B. Clue 6 then forces B into seat 5, which puts D in seat 6 and F in seat 2.

The row from left to right is A, F, C, E, B, D.

Notice what clue 6 does. Without it, B could also sit in seat 6 with D in seat 5, and the puzzle would have two answers. When you seem to have two arrangements, look for the clue you have not used yet.

When some people face south, towards you as you look at the row, their left and right are the reverse of a north-facing person's. Keep the seat numbers fixed and flip the arithmetic instead.

ClueFacing northFacing south
Seat immediately to X's rightX + 1X − 1
Seat immediately to X's leftX − 1X + 1

Phrases that do not use left or right, such as "neighbours", "between" or "at an end", do not depend on the facing direction.

Worked example 2: five people, two directions

J, K, L, M and N sit in a row. Some face north and some face south.

  1. L sits in the middle and faces south.
  2. K sits immediately to the right of L.
  3. N sits immediately to the left of L.
  4. N faces north, and M sits immediately to the right of N.
  5. J sits at an extreme end and faces the same direction as N.
  6. K and M face the opposite direction to N.

Solution. L is in seat 3 facing south, so L's right is seat 2 and L's left is seat 4. That puts K in seat 2 and N in seat 4. N faces north, so N's right is seat 5, where M sits. J takes the last seat, 1. J faces north like N; K and M face south.

The row is J (north), K (south), L (south), N (north), M (south). Because K faces south, the person to K's immediate left is in seat 3, which is L.

Shorter questions skip the puzzle and ask only about positions in a row. Two rules cover nearly all of them.

Total = position from left + position from right − 1

Worked example 3: the length of the row

If Q is 7th from the left and 12th from the right, the row has 7 + 12 − 1 = 18 people. Q is counted from both ends, so one is subtracted.

To count the people between two others, first convert both positions to the same end.

Worked example 4: people between two others

In a row of 10, U is 5th from the left and V is 3rd from the right. V is 10 − 3 + 1 = 8th from the left.

The people between seats 5 and 8 number 8 − 5 − 1 = 2.

  • ✘ Using your own left and right for a person who faces south.
  • ✘ Placing a relative clue before the fixed clues it depends on.
  • ✘ Forgetting to subtract one when a person is counted from both ends.
  • ✘ Stopping with two possible rows when a clue is still unused.

Circular tables follow the same method with a twist; see circular seating arrangement. Position counting is also covered in order and ranking, and puzzles with floors in floor puzzles.

Q1. In puzzle 1 on this page (A, B, C, D, E and F in a row facing north), who sits between C and B? easy

✅ Answer: (b) E

💡 Explanation: The final row from left to right is A, F, C, E, B, D. C is in seat 3 and B in seat 5, so the only person between them is E in seat 4.

Q2. In puzzle 1 on this page, who sits at the right end of the row? medium

✅ Answer: (d) D

💡 Explanation: B must sit next to D and cannot be at an end, so B takes seat 5 and D takes seat 6, the right end for people facing north.

Q3. In puzzle 2 on this page (J, K, L, M and N, some facing north and some south), who sits immediately to the left of K? hard

✅ Answer: (a) L

💡 Explanation: K faces south, so K's left is the seat with the higher number. K is in seat 2, so K's immediate left is seat 3, where L sits.

Q4. In a row, P is 9th from the left end and 14th from the right end. How many people are in the row? easy

✅ Answer: (c) 22

💡 Explanation: P is counted once from each end, so the total is 9 + 14 − 1 = 22. Adding without subtracting one gives the trap answer 23.

Q5. In a row of 25 students, R is 8th from the left end. What is R's position from the right end? easy

✅ Answer: (b) 18

💡 Explanation: Position from the right = total − position from the left + 1 = 25 − 8 + 1 = 18.

Q6. In a row of 30 people, X is 10th from the left end and Y is 12th from the right end. How many people sit between X and Y? medium

✅ Answer: (a) 8

💡 Explanation: Y is 30 − 12 + 1 = 19th from the left. The people between seats 10 and 19 are 19 − 10 − 1 = 8.

Does left mean my left or the person's left?

In seating questions left and right always mean the left and right of the person being described. For someone facing north, that matches your left and right as you look at the diagram from behind the row. For someone facing south it is the opposite.

What if a clue leaves two possible seats?

Draw both cases as separate rows and carry them forward. Later clues usually make one of them impossible. Do not guess one case and hope; if a branch reaches a contradiction, cross it out and continue with the other.

All problems and solutions on this page are original. No outside facts are relied on; every numeric answer is recomputed by software before publishing.

How this page was prepared. Drafted with AI assistance (Claude (Anthropic AI model)) from the sources listed above. 8 calculations on this page were recomputed by software and matched. Automated checks also covered structure, internal links and duplicate text. Software checks cannot confirm facts. Reviewed by praveenkumar on 2026-10-23 against the sources listed above.

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