Seating Arrangment: Introduction

In reasoning based on seating arrangement, we arrange objects or people in different patterns like linear, circular, rectangular following the given set of conditions or constraints.

Here a few tips that can help solve seating arrangement questions:

1. Use the direct clues first. Direct clues are the ones that tell us the position of the object or person in the arrangement directly, without us having to figure it out. For example, in a linear arrangement of four persons – A, B, C, and D, a direct clue can be that A sits on the third position from the left.

2. As you go through the clues, make their visual representation so that you don’t have to read again.

3. Keep track of the people/object who should be together and who should not be together in the arrangement.

Let’s see some examples.

Seating Arrangement Question 1: Answer the questions based on the following information.

A, B, C, and D are to be seated in a row. But C and D cannot be together. Also, B cannot be at the third place.

1. Which of the following must be false?

A. A is at the first place.

B. A is at the second place.

C. A is at the third place.

D. A is at the fourth place.

2. If A is not at the third place, then C has which of the following option?

A. The first place only

B. The third place only

C. The first and third place only

D. Any of the places

3. If A and B are together, then which of the following must be necessarily true?

A. C is not at the first place

B. A is at the third place

C. D is at the first place

D. C is at the first place

Solution:

> B cannot be at the third place.

This implies that B can be first, second or fourth place. Thus, there are three possibilities:

> C and D cannot be together.

1. A cannot be at the first place. So, A is the correct option.

2. If A is not at the third place, C can at the first and third place only. So, C is the correct option.

3. If A and B are together (Case 2(a)), then A must sit at the third place. So, B is the correct option.

Seating Arrangement Question 2: Refer to the data below and answer the questions that follow.

A group of 7 people, Salman, Shahrukh, Aamir, Ranbir, Imran, Shahid, and Akshay are to be arranged in a row of 7 chairs (not necessarily in the same order), such that two adjacent chairs are facing opposite directions but not facing each other.

Given below are some of the conditions to be followed for the seating arrangement:

I. Akshay sits in a chair whose direction is opposite to that of Imran.

II. None of Salman, Shahrukh, or Aamir can sit adjacent to each other.

III. Ranbir and Shahid are best friends, so they always sit together.

IV. Imran has 4 people sitting to his right.

V. Aamir is sitting two positions to the right of Ranbir.

1. Which of the following can never occupy adjacent chairs?

A. Akshay and Imran

B. Ranbir and Salman

C. Shahrukh and Shahid

D. Aamir and Imran

2. If Ranbir is 3 places to the right of Imran, then who is 2 places to the left of Akshay?

A. Salman

B. Aamir

C. Either Shahrukh or Salman

D. Either Aamir or Shahrukh

3. If Akshay is 3 places to the left of Shahid, then who can occupy the corner positions (in any order)?

A. Salman and Aamir

B. Shahrukh and Salman

C. Shahrukh and Aamir

D. None of the above

4. Whose position is always fixed?

A. Imran

B. Akshay

C. Shahid

D. None of the above

Solution:

> Imran has 4 people sitting to his right.

There are two possible arrangements:

> Ranbir and Shahid always sit together. Aamir is Sitting two positions to the right of  Ranbir. None of Salman, Shahrukh, or Aamir can sit adjacent to each other. Akshay sits in a chair whose direction is opposite to that of Imran.

1. Shahrukh and Shahid can never occupy adjacent chairs. So, C is the correct option.

2. If Ranbir is 3 places to the right of Imran, then Aamir sits 2 places to the left of Akshay. So, B is the correct option.

3. If Akshay is 3 places to the left of Shahid, then Salman and Shahrukh occupy the corner places. So, B is the correct option.

4. Imran’s position would depend on the way the chairs are arranged. So, no one’s position is fixed. Therefore, D is the correct option.

Seating Arrangement Question 3: Study the following information and answer the given questions.

Eight friends A, B, C, D, L, M, N, and O are seated in a straight line, but not necessarily in the same order.

> Some of them are facing North while some of them are facing South.

> Only three people sit to the left of N. B sits second to the right of N.

> C sits third to the left of O. O is not an immediate neighbor of B. O does not sit at any of the extreme ends of the line. C and O face the same direction (i.e., if C faces North, then O also faces North and vice-versa).

> Both the immediate neighbors of D face North. D does not sit at any of the extreme ends of the line.

> Persons sitting at the extreme ends face opposite directions (i.e., if one person faces North, then the other faces South and vice-versa).

> Both the immediate neighbors of N face the same directions.

> A sits second to the left of L. D faces a direction opposite to L.

1. How many people sit exactly between B and O?

A. More than four

B. One

C. Two

D. Four

E. Three

2. Who among the following represents the immediate neighbors of the persons sitting at the extreme ends of the line?

A. D, O

B. C, D

C. D, M

D. A, L

E. A, M

3. Who among the following faces North?

A. A

B. L

C. O

D. N

E. C

4. Which of the following is true based on the given arrangement?

A. B and C face the same directions

B. None of the given options is true

C. B faces South

D. Only three people face South

E. M sits at one of the extreme ends of the line

5. Who amongst the following sits second to the right of C?

A. A

B. No one as there is only one person sits to the right of C

C. M

D. B

E. L

Solution:

> Only three people sit to the left of N. B sits second to the right of N.

There are two possibilities, one in which N is facing North, and the other in which N is facing South.

> C sits third to the left of O. O is not an immediate neighbor of B. O does not sit at any of the extreme ends of the line. C and O face the same direction (i.e., if C faces North, then O also faces North and vice-versa).

> Both the immediate neighbors of D face North. D does not sit at any of the extreme ends of the line.

> Persons sitting at the extreme ends face opposite directions (i.e., if one person faces North, then the other faces South and vice-versa).

> Both the immediate neighbors of N face the same directions.

> A sits second to the left of L.

This is only possible in Case 1. So, we reject Case 2.

> D faces a direction opposite to L.

1. Three people sit between B and O. So, E is the correct option.

2. D, O are the immediate neighbors of the persons sitting at the extreme ends of the line. So, A is the correct option.

3. N faces North. So, D is the correct option.

4. M sits at one of the extreme ends of the line. So, E is the correct option.

5. A sits second to the right of C. So, A is the correct option.

Let’s practice what we have learned.

Seating Arrangement Practice Exercise 1: Read the following information and answer the questions.

Ten persons namely, Litesh, Pawan, Nitu, Parul, Dinesh, Sheema, Anil, Dharam, Dolly, and Shelly go for a magic show and they all sit on a single row of seats numbered 1 to 10. There are three couples in this group. Each couple has only one child, the child always sits next to its mother. A family (father, mother, and child) always sit together. Sheela, Dolly, Parul, and Sheema are females whereas Anil, Litesh, Pawan, Nitu, Dinesh and Dharam are males.

(i) Dinesh sits on seat number 6 which is immediately next to Nitu’s mother’s seat.

(ii) Sheela sits on a seat whose number is both a perfect square and a perfect cube.

(iii) Dharam is Dolly’s father and they both sit on prime numbered seats.

(iv) Litesh, the bachelor sits next to Pawan.

(v) The children are Nitu, Dolly, and Dinesh.

1. Who is Dinesh’s mother, if the person sitting two places away from the person sitting immediately next to Nitu is Parul?

A. Sheema

B. Sheela

C. Parul

D. Cannot be determined

2. Who is sitting five places to the left of the person who is sitting two places to the left of Dharam’s wife?

A. Litesh

B. Pawan

C. Nitu

D. Cannot be determined

3. What is Anil’s seat number?

A. 4

B. 5

C. 9

D. 10

4. Who is sitting to the immediate right of Litesh? (use data from previous questions, if necessary)

A. Dolly

B. Dharam

C. Pawan

D. Nobody

> There are 10 persons in which 3 are couples and 3 are children.

> A family always sit together. This implies, of the 10 seats, 9 are occupied by the families with each family occupying 3 consecutive seats.

> The child always sits next to his mother.

> The children are Nitu, Dolly, and Dinesh.

(i) Dinesh sits on seat number 6 which is immediately next to Nitu’s mother seat.

This implies Nitu’s mother can either sit on seats number 5 or 7. If she sits at seat number 5, Nitu and his father would occupy seats numbered 4 and 3 respectively. In that case, it won’t be possible for all the three families to occupy 3 consecutive seats. This does not happen if Nitu’s mother sits on seat number 7.

(ii) Sheela sits on a seat whose number is both a perfect square and a perfect cube.

This implies Sheela sits on seat number 1.

(iii) Dharam is Dolly’s father and they both sit on prime numbered seats.

The only possibility is both of them occupying seats with numbers 2 and 3. Therefore, Sheela must be Dolly’s mother and hence, Dolly would occupy seat number 2.

(iv) Litesh, the bachelor sits next to Pawan.

Seat number 4 would be occupied by Dinesh’s father. Therefore, Pawan must be Nitu’s father and would sit on seat number 9. This implies Litesh sits on seat number 10. Anil must be Dinesh’s father and would sit on seat number 4.

1. The person sitting two places away from the person sitting immediately next to Nitu is Parul.

> If we consider the person sitting next to Nitu to be the one with seat number 7, then Parul would occupy seat number 5.

> If we consider the person sitting next to Nitu to be the one with seat number 9, then Parul would occupy seat number 7.

Therefore, we cannot determine who among Parul and Sheema occupies seat number 5. So, D is the correct option.

2. Dharam’s wife is Sheela. The actual arrangement must be the reverse of what we have made (that is, seat number 1 is at the right end and seat number 10 is at the left end).

Therefore, Dharam is sitting two places to the left of Sheela and Nitu is sitting five places to the left of Dharam. So, C is the correct option.

3. Anil sits on seat numbered as 4. So, A is the correct option.

4. From the second question, we know that the actual arrangement must be the reverse of what we have made (that is, seat number 1 is at the right end and seat number 10 is at the left end). Therefore, Pawan is sitting to the immediate right of Litesh. So, C is the correct option.