Seating arrangement and puzzles

In short

Seating arrangement and puzzle questions give a set of conditions about where people sit (in a row, around a table, in two rows) and ask who sits where, who is a neighbour, or how many people sit between two of them. They test whether a candidate can hold several constraints in mind at once, fix the certain information first, and work through the remaining possibilities without guessing. Every major Indian recruitment test uses them: TCS NQT, Infosys, Wipro, Capgemini, Accenture, AMCAT, eLitmus, CoCubes, and the banking and insurance exams (IBPS PO/Clerk, SBI PO, RRB, LIC AAO) where a single set carries 4-5 marks. CAT, XAT and the CSAT paper of the UPSC Civil Services exam also use them in a harder, data-heavy form. The skill is examined as "analytical reasoning" or "logical ability" in university CBCS soft-skills and quantitative-aptitude papers.

Explained

The arrangement types

• Linear (single row): people sit in a line facing a stated direction - usually north (so the arranger's left is the west end) or south (left and right flip). Positions are numbered 1 to n from one end.
• Circular: people sit around a circle, table or round bench, facing the centre (the default) or facing outside. There are no ends, so every position is relative - you fix one person arbitrarily and place the rest with respect to that person.
• Rectangular / square table: seats on each side; corners may face the centre while middle seats face outwards (or the reverse) - read the statement, never assume.
• Double row (parallel rows): two rows of equal size facing each other; a person in row 1 faces a person in row 2. Row 1 typically faces north and row 2 faces south, or vice versa.
• Mixed-facing: some face the centre and some face outside in the same circle - the hardest common variant, because "immediate left" changes meaning seat by seat.
• Comparison puzzles tied to seating: the arrangement is combined with a second variable (city, salary, department, car colour) - solved with a grid alongside the seating diagram.

Direction conventions - the single biggest source of error

• Facing north in a row: the person's left is west, right is east. Facing south: left is east, right is west.
• Facing the centre of a circle: going clockwise means moving to each person's left; anticlockwise means moving to their right.
• Facing outside the circle: this reverses - clockwise is to their right, anticlockwise is to their left.
• In a double row, if A (row 1) faces B (row 2), then A's left side is B's right side - the person on A's immediate left faces the person on B's immediate right; a shift to A's right is a shift to B's left.
• Always draw the diagram once with a small arrow on each seat for the facing direction, and mark the compass on the page.

Reading the clue language precisely

• "Immediate left of A" - the seat adjacent to A on A's left, from A's own point of view, not the solver's.
• "To the left of A" (without "immediate") - somewhere on A's left side, distance unknown.
• "Third to the left of A" - count three seats leftwards from A; the answer seat is the third one.
• "Between A and B" - A and B are the boundaries; a count "three persons sit between A and B" excludes A and B.
• "A sits third from the left end" - position 3 counting from the left end; "third from one of the ends" - position 3 or position n−2, two cases.
• "A and B are neighbours" - either order (A-B or B-A), so it is a block of two with two internal arrangements.
• "Exactly two persons sit between A and B" - distance 3 between their positions; "at most two" - distance 1, 2 or 3; "at least two" - distance ≥ 3.
• "A is not adjacent to B" - a negative clue; it does not place anyone but eliminates arrangements, so use it last.
• "A faces the person who sits second to the right of B" - resolve the inner description first, then the facing link.

A step-by-step method

1. Count the people and the seats. Note whether n people fill n seats exactly (most sets) or seats are vacant.
2. Draw the frame - n blanks in a row, or a circle with n marked positions, with facing arrows.
3. Classify every clue into: (a) definite - fixes a person to a seat or a fixed gap; (b) relative - fixes two people to each other; (c) negative - rules something out.
4. Place the definite clues first. A clue naming an end, a position number, or a position relative to an end is gold - use it before anything else.
5. Build blocks from relative clues: "P is second to the right of Q" is a rigid 3-seat block Q _ P that can slide along the frame.
6. Enumerate the cases. Where a block fits in two or three places, draw each case as a separate diagram - do not try to hold them mentally.
7. Apply negative clues to kill cases. Each contradiction eliminates one diagram.
8. Finish with elimination: the people not yet placed go into the seats not yet filled; if only one seat is left for one person, that is forced.
9. Verify every clue against the final diagram before answering, including the ones already used - a misread clue usually shows up here.
10. Answer only what is asked - many sets ask "how many between", not "who sits there".

Counting rules in arrangements

• In a row, if A is at position p and B at position q, the number of persons strictly between them is |p − q| − 1.
• Position from the other end: if there are n seats and a person is p-th from the left, they are (n − p + 1)-th from the right.
• In a circle, two people split the remaining n − 2 into two arcs; "three persons between A and B" is ambiguous unless a direction is stated, so both arcs must be tested - a very common trap.
• Opposite seats exist only for an even n in a circle: the person opposite position p is p + n/2 (wrapping around).
• Distinct circular arrangements of n people = (n − 1)!; if clockwise and anticlockwise (mirror-image) arrangements are treated as the same, divide by 2.
• Degrees per seat in a circle of n equally spaced seats = 360/n - occasionally asked as "A sits 90° clockwise from B".

Puzzle families beyond pure seating

• Blood-relation seating: the circle contains a family and the clues mix seats with relationships - solve the family tree separately, then map it onto seats.
• Day / month / designation puzzles with a seating layer: each person has a seat and a second attribute; use a two-column grid beside the diagram.
• Comparison-based puzzles: heights, ages, marks or salaries with ">" style clues - order them on a line first; seating conditions then slot onto that order.
• Vacant-seat puzzles: n seats and fewer than n people, so the empty seats are themselves unknowns - count seats, not people, when applying gap clues.
• Selection / team puzzles: choose members subject to "if X then not Y" rules - closer to syllogistic reasoning but routinely set with seating in the same block.
• Note: floor-wise, box-stacking and day-scheduling arrangements are a separate family and are treated under their own topic.

Advantages, limits and exam strategy

• Why employers test it: the question needs no formula or domain knowledge, so it measures structured thinking, patience and accuracy rather than prior coaching on content.
• Limits: a single early misreading corrupts the whole set, so the marks are "all or nothing" - a 4-5 mark set is lost entirely by one direction error.
• Time budget: 4-6 minutes for a 5-question set in a banking exam; in a campus test, roughly 60-90 seconds per question. If no definite clue exists after two minutes, leave the set and return.
• Sectional cut-offs: IBPS/SBI prelims and mains have sectional cut-offs for reasoning, so leaving every puzzle is not viable - attempt the set with the most definite clues first.
• Negative marking: IBPS and SBI deduct 0.25 of a mark for a wrong answer, and eLitmus penalises wrong answers; TCS NQT, AMCAT and most other campus platforms currently do not (check each year's notification, as patterns change), so on a penalised paper a half-solved diagram should not be guessed across all five questions.
• Scratch work matters: most online test platforms give rough sheets or an on-screen scratchpad - redrawing the diagram cleanly is faster than editing a messy one.

Key points

• Linear arrangement - people in a row facing one stated direction; positions numbered from an end.
• Circular arrangement - no ends; fix one person as the reference and place all others relative to that person.
• Facing centre - clockwise = each person's left; facing outside - clockwise = each person's right.
• Facing north in a row - left is west; facing south - left is east.
• Immediate left/right - adjacent seat; without "immediate", only the side is known, not the distance.
• "Between" excludes the boundary people - "k persons between A and B" means positions differ by k + 1.
• Definite clue - fixes a seat or an end; always placed before relative clues.
• Block - a rigid group from a relative clue that slides along the frame until a definite clue anchors it.
• Negative clue - never places anyone; used only to eliminate drawn cases.
• Case enumeration - when a block fits in more than one spot, draw every case separately; never hold cases in the head.
• Position conversion - p-th from left = (n − p + 1)-th from right in a row of n.
• Persons between in a row = |p − q| − 1.
• Opposite seat - exists only for even n; opposite of p is p + n/2 (wrap around).
• Circular count ambiguity - "x persons between A and B" in a circle has two arcs unless a direction is given.
• Circular arrangements of n distinct people = (n − 1)!; divide by 2 if reflections are identical.
• Double row - A in row 1 facing B in row 2; a shift to A's right is a shift to B's left.
• Verification - re-check all clues against the finished diagram before marking answers.
• All-or-nothing scoring - one misread direction loses the whole 4-5 mark set.

Formulas and examples

Example 1 - row length from two positions. In a row of students facing north, Anu is 7th from the left end and 12th from the right end. How many students are in the row, and how many sit between Anu and Ravi, who is 4th from the left?

• Total = 7 + 12 − 1 = 18 students.
• Anu at position 7, Ravi at position 4 → persons between = |7 − 4| − 1 = 2 students.
• Anu's position from the right = 18 − 7 + 1 = 12, which matches the given data, so the count is consistent.

Example 2 - a full linear set. Six friends - P, Q, R, S, T, U - sit in a row facing north. (i) P sits at one of the ends. (ii) Q sits third to the right of P. (iii) R sits immediately left of T. (iv) S sits second to the left of U. (v) U does not sit at an end.

• Seats 1-6 from the left. Case A: P at seat 1 → Q at seat 4 (1 + 3).
• Clue (iv): S two left of U → (S, U) can be (2,4), (3,5) or (4,6). Seat 4 is Q, so (S,U) = (3,5); U at 5 is not an end, so this holds.
• Remaining seats 2 and 6 for R and T, with R immediately left of T - seats 2 and 6 are not adjacent, so Case A fails.
• Case B: P at seat 6 → Q must be three to P's right, which runs off the row; so P at seat 6 is impossible and the only end left is seat 1 - already shown to fail. Re-examine: "third to the right of P" with P at the right end is invalid, so clue (ii) forces P at seat 1, 2 or 3; combined with (i), P = seat 1.
• The set as stated therefore has no valid arrangement - the contradiction is the answer. This is exactly what step 9 of the method catches: contradiction found in verification means a clue was misread or the data is inconsistent. Replacing (iii) with "R sits immediately left of T or T immediately left of R" still fails, since seats 2 and 6 are never adjacent - so the inconsistency is real, not a reading error.

Example 3 - the same set made consistent. Keep clues (i), (ii), (iv), (v) and replace (iii) with "T sits at the extreme right end".

• P at seat 1, Q at seat 4, S at seat 3, U at seat 5, T at seat 6 → R takes seat 2.
• Final row (left to right): P, R, S, Q, U, T.
• Checks: Q is third right of P (1 → 4); S is second left of U (3 → 5); U at 5 is not an end. All clues hold.
• Persons between R and U = |2 − 5| − 1 = 2 (S and Q). R's position from the right end = 6 − 2 + 1 = 5th.

Example 4 - circular, facing the centre. Eight people - A to H - sit around a circular table facing the centre, equally spaced. A sits opposite E. B sits second to the right of A. C sits immediately left of E. D sits third to the left of A.

• Number the seats 1-8 clockwise. Fix A at seat 1. Facing the centre, clockwise = to each person's left, anticlockwise = to their right.
• A opposite E → E at seat 1 + 8/2 = seat 5.
• B second to A's right = two seats anticlockwise = 1 → 8 → seat 7.
• C immediately left of E = one seat clockwise from 5 = seat 6.
• D third to A's left = three seats clockwise from 1 = seat 4.
• Seats left: 2, 3, 8 for F, G, H in any order → 3! = 6 possible arrangements, so the set is under-determined and only questions about A, B, C, D, E can be answered definitely.
• Gap between B (7) and D (4) = min(|7 − 6 + 3|, …) → min(|7 − 4|, 8 − 3) = min(3, 5) = 3 seats apart, i.e. 2 persons between them on the shorter arc (seats 6 and 5 - C and E).
• Angle per seat = 360/8 = 45°, so B sits 90° anticlockwise from A.

Example 5 - double row. Five people (A-E) in row 1 face north; five (P-T) in row 2 face south; each row-1 person faces a row-2 person. A sits at the extreme left of row 1 (as seen by the solver). C faces R. R sits second to the right of P, who is at an end of row 2.

• Row 2 faces south, so its left (from the solver's view) is its occupants' right. Number both rows 1-5 from the solver's left; row-1 seat k faces row-2 seat k.
• P at an end of row 2 and R two to P's right: facing south, P's right is the solver's left, so from solver-seat 5, two to P's right = solver-seat 3. (If P were at solver-seat 1, two to P's right would run off the row.) So P = seat 5, R = seat 3.
• C faces R → C = row-1 seat 3. A is at row 1 seat 1.
• Seats 2, 4, 5 of row 1 go to B, D, E (3! = 6 ways) and seats 1, 2, 4 of row 2 to Q, S, T (6 ways) - again partially determined, which is normal in a 5-question set where only some questions are answerable.

Where it is used

• Banking and insurance recruitment: IBPS PO/Clerk, SBI PO/Clerk, RBI Grade B, NABARD and LIC papers devote 15-25 of the reasoning marks to puzzle and seating sets.
• IT campus hiring: TCS NQT, Infosys, Wipro Elite, Capgemini, Accenture, Cognizant and the AMCAT / eLitmus / CoCubes platforms screen on logical ability sets of this kind before the technical round.
• Management and civil-services entrance: CAT and XAT logical reasoning blocks, and the UPSC CSAT (Prelims Paper II) analytical-reasoning questions.
• Analyst and consulting roles: scheduling staff across shifts, allocating desks or seats in an office move, assigning interview panels - the same constraint satisfaction done on a spreadsheet.
• Software work: constraint-satisfaction logic appears directly in timetable generators, exam-seating allocation software used by Indian universities, airline and theatre seat maps, and SQL/array index arithmetic where off-by-one errors are the same mistake as a mis-counted "between".
• Group discussion and HR rounds: interviewers use a short puzzle to watch how a candidate structures an unfamiliar problem aloud, not whether the answer arrives fast.

Interview questions

• Q: In a circle facing the centre, does clockwise movement go to a person's left or right? A: To their left; if they face outside the circle, clockwise goes to their right.
• Q: A person faces north in a row - which compass direction is their left? A: West; if they face south, their left is east.
• Q: "Three persons sit between A and B" - how far apart are their seat numbers? A: Four seats apart in a row, because the three people in between are excluded: |p − q| = 4.
• Q: Why is "two persons between A and B" ambiguous in a circular arrangement? A: Because the two people could lie on either arc between A and B, so both cases must be drawn unless a direction (clockwise or anticlockwise) is stated.
• Q: If a person is 9th from the left and 8th from the right, how many people are in the row? A: 9 + 8 − 1 = 16, subtracting one because that person is counted in both positions.
• Q: How many distinct ways can 7 people sit around a round table? A: (7 − 1)! = 720; if clockwise and anticlockwise arrangements are considered the same, 360.
• Q: Which clue would you use first in a long puzzle set, and why? A: The most definite one - a clue fixing someone to an end or a numbered seat - because it anchors the frame and converts relative clues into fixed positions.
• Q: What do you do with a negative clue such as "A is not next to B"? A: Keep it aside and apply it after drawing the possible cases; it eliminates arrangements but never places anyone.
• Q: In a double row, A in row 1 faces B in row 2 - if someone sits to A's right, where are they relative to B? A: To B's left, because the two rows face opposite directions, so the left-right sense reverses across the rows.
• Q: How do you handle a set with 8 seats but only 6 people? A: Treat the two vacant seats as unknown objects and apply all gap and "between" clues to seats, not to people.
• Q: You reach a contradiction at the last clue - what does that mean? A: Either a clue was misread or an earlier case was not eliminated properly; redraw from the definite clues rather than patching the existing diagram.
• Q: Only three of five questions in a set are answerable from your diagram - what next? A: Answer those three and leave the rest; where negative marking applies (0.25 in IBPS/SBI), guessing on an under-determined set loses more than it gains.

Common mistakes

• Reading "left" from the solver's point of view instead of the seated person's - the single most common error, and fatal in circular and facing-outside sets.
• Forgetting that "facing outside" reverses clockwise and anticlockwise, and that row 2 of a double row reverses left and right.
• Including A and B when counting "persons between A and B", giving an answer one too many.
• Treating a circular "k persons between" clue as unique instead of testing both arcs.
• Starting with relative or negative clues and building a diagram with no anchor, then rebuilding from scratch under time pressure.
• Holding two or three possible cases mentally instead of drawing them, then mixing conclusions from different cases.
• Not re-verifying all clues at the end, so a set that was solved on a misread clue yields five wrong answers.
• Spending eight or ten minutes on one stubborn set and losing easier marks elsewhere in the section.

Related topics

Floor, box and scheduling puzzles · Blood relations · Direction sense · Inequalities · Syllogisms · Data sufficiency