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Sitting Arrangement

Reasoning · Verbal Reasoning

8 Part3 worked examples12 practice questions

Imagine six friends must sit on one bench and all you know is: “Ravi is at the extreme right”, “Seema is immediately to the left of Ravi”, “there is exactly one person between Aman and Seema”… Finding the order of the whole bench from such facts is Sitting Arrangement. It is a kind of puzzle in which every clue fixes a little more of the seating.

In the exam the same puzzle comes in many forms: a straight row, around a round table, a square table, two rows facing each other, or the floors of a building. Sometimes each person also has one more fact attached, such as a favourite colour. The method is the same in every form: first build the whole seating, then read the answer to the question from it.

In this chapter we start from zero: first the right meaning of “left” and “right” (the biggest source of mistakes), then the language of clues, then a five-step method of building the seating. After that we take one shape at a time and finally practise everything mixed. In every puzzle the clues are chosen so that the seating has exactly one solution.

How to use this chapter

  1. Read — each part first explains the idea, then the method.
  2. Study the solved example — in the “Example” boxes you can watch the clues being applied one by one, and a picture of the finished seating follows.
  3. Try it yourself — solve the “Try it yourself first” puzzles on paper: draw the empty seats, fill in the clues, then pick an option. The solution also shows how much of the seating is filled after each clue.
  4. Know the level — Basic, Standard, Advanced. In basic puzzles every clue tells you straight where the next person is; in advanced ones you must combine two clues.
NoteThe questions you have solved are remembered in this browser. Look at the panel on the right (the “Contents” button on a phone) to see how many you have got right.
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Foundation — left-right, vocabulary and method

Every puzzle rests on these three things

How facing decides left and right, the meaning of clue phrases, counting formulas and the five-step method.

Left and right — whose?

Each person’s own left and right, decided by where he faces

How facing decides the direction of the left and right hands, and why persons facing each other have opposite sides.

The commonest way of losing marks in these questions is to decide “left” and “right” from the reader’s own place. The rule is one only: “to the left of X” means — the side where X’s own left hand is. Imagine you sit in X’s chair and look the way X looks.

Every person has four sides: the front (where the face looks), the back, the left and the right. In the figures below the arrow (F) is in front of X; L is his left and R his right hand. The first figure shows a person facing North, the second one facing South. Watch the places of L and R — they swap.

XFLRN
Facing North: the left hand points West (left side of the picture), the right hand points East
XFLRS
Facing South: the left hand points East, the right hand points West
FacesLeft handRight hand
NorthWestEast
SouthEastWest
EastNorthSouth
WestSouthNorth
TrickA trick to remember: on a map North is up and West is on the left. Stand facing North and West falls on your left hand, East on your right — just like the map. Get the others by turning this round: for a person facing South swap both.

Two persons facing each other

When two persons face each other their sides swap: the direction of one person’s left hand is the direction of the other person’s right hand. That is why, in puzzles with two rows facing each other, the “left end” of one row lies opposite the “right end” of the other. This will matter a lot in the part on rows facing each other.

Example 1 · Basic
A person stands facing East. In which direction does his left hand point?
Solution, step by step
  1. 1He faces East, so East is in front of him.
  2. 2Draw it: North up, East to the right. For someone looking East, up (North) is his left side and down (South) his right side.
  3. 3So the left hand points North. (Check: turn 90° to the left from East and you face North.)
Answer North
Drawing a small picture is always the safest.
BasicTry it yourself first
A person stands facing North. In which direction does his left hand point?
BasicTry it yourself first
A person stands facing South. In which direction does his right hand point?
StandardTry it yourself first
A person stands facing South. In which direction does his left hand point?
StandardTry it yourself first
Qasim and Vandana stand facing each other, and Qasim faces North. The left hand of Qasim points in the same direction as which of the following?

The language of clues and counting formulas

The exact meaning of every phrase

All phrases on one example row, and the formulas for left and right places, persons between and the total.

Clues are always written in a few fixed phrases. You must know their exact meaning, because one word more or less moves a person. Below is an example row in which six persons P Q R S T U sit from left to right, all facing North.

PQRSTULR↑ N
In the picture L and R are the persons’ own left and right ends (all face North, so left = West)
PhraseMeaningIn P Q R S T U
at the left / right endthe first / last seat of the rowP at the left end, U at the right end
immediately to the right of Xthe seat right next to X on his rightQ is immediately to the right of P
second to the right of Xtwo steps right of X (one person in between)R is second to the right of P
third from the left endcounting starts at the left endR is third from the left end
exactly between Y and ZY and Z are right next to him on both sidesR is exactly between Q and S
k persons between X and Ythe count between them (they themselves are not counted)There are 2 persons (Q, R) between P and S
somewhere to the right of Ya loose clue — need not be next to himT is to the right of Q (R and S lie between)
sit next to each otherneighbours of each other — which side is not saidQ and R are neighbours; Q and S are not
Note“Exactly between” and “k persons between” are different things. “R is exactly between Q and S” means Q-R-S side by side. “There is one person between Q and S” means Q ? S — who is in the middle is not decided by that clue. Read the words carefully.

Three counting formulas

Suppose the row has n persons. A person is L-th from the left end and R-th from the right end. Then:

The two places always add up to one more than the total (the person is counted in both counts).
place from the left
place from the right
total persons
Persons between those at places p and q from the left (q > p) — the two themselves are not counted.
Number of persons to the right of the L-th person from the left (there are L − 1 to his left).
Example 2 · Basic
In a row of 25 children Rita is 8th from the left. What is her place from the right, and how many children are to her right?
Solution, step by step
  1. 1Formula: L + R = n + 1, so 8 + R = 26 and R = 18.
  2. 2Children to her right = n − L = 25 − 8 = 17. (Check: 18th from the right means 17 children are to her right — it agrees.)
Answer 18th from the right; 17 children to her right
persons to the right = place from the right − 1
BasicTry it yourself first
38 children stand in a row. Varun is 29th from the left. What is Varun's place from the right?
BasicTry it yourself first
In a row of 26 persons, Kiran is 14th from the left and Dinesh is 22nd from the left. How many persons are between the two?
StandardTry it yourself first
In a row of 32 persons Aman is 23rd from the left. How many persons are to the right of Aman?
StandardTry it yourself first
In a row, Farooq is 19th from the left and 14th from the right. How many persons are there in the row?
AdvancedTry it yourself first
In a row, Jaya is 7th from the left and Chetan is 10th from the right. After they exchange seats, Jaya becomes 11th from the left. How many persons are in the row?

The five-step method of building the seating

Shape → empty seats → certain clues → pairs → loose clues and check

The method that fits every puzzle, the five kinds of clues and the order in which to use them.

The seating does not appear the moment you read the clues. But with a firm order even the hardest puzzle opens step by step.

Five steps
1. Shape and facing2. Draw empty seats3. Certain clues first4. Pairs and blocks5. Loose clues + check
  1. Shape and facing — a row, a round table or two rows? Which way does everyone look? It is written in the first line; left and right depend on it.
  2. Draw the empty seats — n boxes for a row, n circles for a table. Mark the facing with arrows on them.
  3. Certain clues first — clues that name one seat outright (“at the right end”, “third from the left”) go in first. Everything else hangs on them.
  4. Pairs and blocks — clues like “X is immediately to the left of Y” make small blocks (like [Y X] together). Then see where the block can fit in the row.
  5. Loose clues and check — clues like “somewhere to the left” or “not next to” cut out wrong options. Finally test every clue once on the finished seating.
Kind of clueExampleWhat to do
Certain (names a seat)“A is at the left end”, “B is fourth from the left”Fill in directly
Pair (neighbour fixed)“C is immediately to the right of A”Place next to the person whose seat you know
Distance (k steps)“D is third to the right of A”Count k steps and place
Loose (somewhere)“E is somewhere to the left of B”Use at the end, to pick among the seats left
Negative (what is not)“F does not sit next to A”Strike out one option

Below is the first complete example. Notice how many seats are certain after every clue (· means not decided yet), and the picture of the finished seating at the end.

Example 3 · Basic
Five persons H, L, S, V, X are sitting in a row. All of them face North. (Left and right mean each person's own left and right.) (i) S sits immediately to the left of L. (ii) H sits immediately to the left of V. (iii) L sits at the extreme right end. (iv) V sits second to the left of L. Question: Who sits at the left end of the row?
Solution, step by step
  1. 1Draw five empty seats: _ _ _ _ _ . All face North, so the left hand points West and left-right in the picture stay as they are.
  2. 2Clue (4) “V sits second to the left of L” gives: · · · · ·
  3. 3Clue (2) “H sits immediately to the left of V” gives: · · · · · — no new seat is certain yet, but only 4 arrangements are still possible.
  4. 4Clue (1) “S sits immediately to the left of L” gives: · · · · · — no new seat is certain yet, but only 2 arrangements are still possible.
  5. 5Clue (3) “L sits at the extreme right end” gives: X H V S L — now the arrangement is completely fixed.
  6. 6The full arrangement: X H V S L (left → right, all facing North)
  7. 7At the left end is X.
Answer X
First build the whole arrangement from the clues; only then read off the answer.
XHVSLLR↑ N
The solved arrangement

Puzzle — Row arrangement. Five persons B, D, G, H, W are sitting in a row. All of them face North. (Left and right mean each person's own left and right.) Read the clues below and answer the questions.

  1. H sits second to the left of B.
  2. G sits immediately to the right of D.
  3. B sits third from the right end.
BasicTry it yourself first
Who sits at the left end of the row?
BasicTry it yourself first
Who sits immediately to the left of D?
BasicTry it yourself first
How many persons sit between D and H?
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A straight row and floors

The commonest shape — people sitting in one line

Chains of direct clues, relative and loose clues, direction and interchange questions, and floors of a building.

Direct clues — build the chain link by link

Start from one certain seat and add one person at a time

When every clue puts a new person relative to one already known, the puzzle opens like a chain.

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Relative and loose clues — between, how many, somewhere

When both names are unknown, build blocks

How to use “exactly between”, “k persons between”, “somewhere to the left” and “not next to”, and the sliding-block method.

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Direction questions and interchanges

North-facing or South-facing — and “they exchange seats”

Fixing the western and eastern ends from the facing, and reading the answer from the new row after seats are exchanged.

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Floors of a building and shelves

Stand the row upright: left end = bottom

How to turn an above-below arrangement into a row, and how to count “k-th floor from the top”.

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Round and square tables

Where the row has no ends

Clockwise, facing the centre or outside, mixed facing, and the corners and sides of a square table.

Round table — everyone facing the centre

Left = clockwise, right = anticlockwise

The left-right rule at a round table, counting the person opposite, and how to start the puzzle.

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Facing outside and mixed facing

Turn the face round and left and right swap

Left and right for those facing outside, and when some face in and some face out.

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Square and other shaped tables

Corners face out, side-middles face in — understand this facing rule first

The seats of a square table, the facing of corners and sides, counting the opposite person, and pentagon, hexagon and rectangle tables.

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Two rows facing each other

Every person has someone exactly in front

Two parallel rows looking at each other: the left and right of each row and the opposite pairs.

Two rows — opposite, beside and the ends

The upper row looks South, the lower row looks North

The opposite sides of left and right in the two rows, what “opposite” means, and the grid for such puzzles.

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5

Seating with one more fact

A colour, job or city belongs to every person

Making two lines of names and choices, and treating the name and choice in the same column as one person.

Names and choices — the two-line method

One seat, two facts

When clues sometimes catch a person by his name and sometimes by his choice, joining the two at the same seat.

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6

Strategy guide

The order of the clues and the slips to avoid

What to do first in any seating puzzle, what to do for each kind of clue, and where slips happen.

Where to begin

See the clue, decide how to use it

What to do with each kind of clue, and the firm order for every puzzle.

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Common traps and time-savers

The mistakes that keep happening

The commonest reasons for losing marks in seating puzzles and how to avoid them.

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7

Mixed practice

All shapes mixed — first spot the shape, then solve

Row, floors, round and square tables, rows facing each other and choice puzzles — in three levels.

Basic practice

Every clue direct — build the chain

Facing and direction, counting formulas and short chain puzzles.

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Standard practice

Blocks, loose clues, round tables and two rows

Rows with blocks and loose clues, a round table of seven, two rows of three and floors.

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Advanced practice

Eight persons, mixed facing, square tables, choices and interchanges

A table with mixed facing, a square table, two rows of four, a choice puzzle and an interchange on a South-facing row.

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8

Revision — cards

Flip each card and test yourself

Think of the answer yourself first, then flip.

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