Seating Arrangements

Introduction

Seating Arrangement problems are very common in many competitive exams of SBI PO, IBPS, RRB, and the reasoning section of tests conducted by Tech giants like TCS and Wipro. These problems are used to judge the reasoning ability of candidates and can sometimes get confusing. In this blog, we will cover some nifty tricks and tips to solve such questions so that you can solve the various types of Seating Arrangements problems with ease in significantly less time.

Types

Seating Arrangement problems revolve around the various arrangements in which people can sit. 

There are mainly five types of seating arrangements:
 

  1. Linear seating arrangement
  2. Double row seating arrangement
  3. Circular seating arrangement
  4. Square / Rectangular seating arrangement
  5. Complex seating arrangement

 

  • Linear seating arrangement:

In this type of arrangement, people are sitting in a single row. This is the simplest type of arrangement. We only need to observe who sits on the left and right of a specific person to answer linear seating arrangement questions.

For example, five people sitting on a straight bench. 

 

 

  • Double row seating arrangement:

Here, people are arranged in two parallel rows, usually facing each other.

For example, consider two benches facing each other with five people sitting on each of the benches. 

  • Circular seating arrangement:

As the name suggests, people are seated around a circle, usually facing towards the centre. But they can also be facing outward of a table. In some complex problems, some people can be seated such that they face towards the center and some face outwards. This is the most popular and most asked variant of the seating arrangement problems.

An example of this can be eight people sitting around a circular table.

 

 

  • Square/Rectangular seating arrangement:

This arrangement is similar to a circular seating arrangement, but people are seated around a square or a rectangle.

  • Complex arrangement: 

In this type of seating arrangement problem, information about people or things is given. We have to map the people/ things given with their interests, information to solve the question. 

For example, consider five friends sitting in a cafe. They can be wearing five different coloured t-shirts and are drinking five varieties of coffee. 

Tip: While solving this type of question, always make a table using the given information.

Tips and Tricks to solve seating arrangement problems

  • Always draw diagrams to understand the problem statement better. In case of complex seating, arrangement problems draw tables.
  • Specific and non-specific information

Specific information: This kind of information is straightforward and can be used in diagrams. E.g. Rohit sits to the right of Mina.

Non-specific information: This kind of information is not at all straightforward and can not be directly used in diagrams. You can keep a list of such non-specific information and use it in the diagram when the right time comes. Do not worry; we will take a few examples of seating arrangement problems, where this idea will get crystal clear.

E.g. Rohit is an immediate neighbour of Mina. This sentence does not specify whether Rohit sits to the left or right of Mina.

  • Start drawing diagrams with the help of specific information first, and once that's done, take the help of non-specific information.
  • While drawing the diagram, try to find statements related to the information that you just used. This will help you come closer to the solution pattern. 
  • To avoid confusion in circular arrangement /square arrangement/ rectangular arrangement problems, assume that the people face the center if nothing is explicitly mentioned.
  • The number of people can be even/odd in a circular arrangement. In the case of an even number of people, draw one pair of people exactly opposite each other to make the problem easier to visualize. 

    In the case of an odd number of people, adjust the remaining one person within the space left.

     

 

  • Be very careful about the direction in which people are arranged in the problem.

    In the case of a linear arrangement,

 


In the case of a circular arrangement,

 

  • Assuming yourself to be the person in the problem can also help you to understand the directions better.
  • If a statement like this is given, ‘A is sitting third to the left of B’ - it implies that 
    • A is sitting towards the left of B
    • There are 2, i.e. (3-1) people sitting between A and B

Question on Linear seating arrangement

Ram, Varun, Avni, Jhotsna, Sonali and Kamlesh are sitting in a row. Sonali and Kamlesh are sitting in the middle of the row next to each other. Varun and Avni are sitting at different ends. Avni is sitting right to Ram. 

Q1. Who is sitting right to Varun?

A. Jhotsna

B. Sonali

C. Kamlesh

D. No one

Ans: A) Jhotsna

Explanation: As no direction is given, let us consider everyone is facing north for our convenience. Six people are given in the problem, as six is an even number, so there will be two people sitting in the middle. According to the problem statement, these two people are Sonali and Kamlesh.

Till now, our diagram should look something like this,

 

Now the problem statement says that Varun and Avni are at the two extreme ends. There are two possibilities here, Avni can either be on the extreme left or the extreme right. So it’s a non-specific detail. We move on to the next statement, which says ‘Avni is sitting right to Ram’; this clears our confusion, and, understandably, Avni has to sit in the extreme right corner to be sitting right to Ram. 

Our diagram now looks this,

We are now left with one vacant place, which is obvious from the above diagram that Jhotsna will occupy it.

 

Question on Double row seating arrangement

Ten people are sitting opposite each other in two parallel rows. Five of them, M, N, O, P and Q, are facing towards the north. The remaining five A, B, C, D and E are facing towards the south. Two people are sitting between M, and P. M sits at one of the extreme ends. P's immediate neighbour faces B. There are two people between B and D. C does not sit opposite to P. A and C are immediate neighbours. Q sits second to the right of N. E sits third to the left of A. 

Q1. Who is the immediate neighbour of Q?

A. D

B. E

C. O

D. B

Ans: C) 

Q2. Who is facing P?

A. A

B. C

C. D

D. E

Ans: A)

Explanation:

List of statements:

  1. Two people are sitting between M and P.
  2. M sits at one of the extreme ends.
  3. P's immediate neighbour faces B. 
  4. There are two people between B and D. 
  5. C does not sit opposite to P. 
  6. A and C are immediate neighbours of each other. 
  7. Q sits second to the right of N. 
  8. E sits third to the left of A. 

The statement of 1 gives us non-specific information so that we will skip to the next statement, i.e., 2. According to 2 there are two possible ways to draw the diagram. M can be at position 1 or 5.

 

 

Now we can place P on both of these diagrams using statement 1. Again there will be two possibilities - P can be placed at position 4 or 2.

 

As we were working with the second row, let us directly skip to statement 7. We can put Q and N only in these two possible positions

Now if we look at statement 3 it says the immediate neighbour of P faces B. We have two neighbours of P, Q and N . Statement 4 says two people sit between B and D. From statement 4 it becomes clear that B will be present either at position 1 for possibility 1 and position 5 for possibility 2. 

 

 

Now according to statement 6, A and C are immediate neighbours. As C cannot sit opposite to P, diagram 1 A will sit in position 4, C will sit in position 3. In the second diagram, A will sit in position 2, and C will sit in position 3.

Now let us fill in the remaining positions of both the rows,

Now according to statement 8, E sits third to the left of A. As we can clearly see in diagram 1, E sits third to the left of A. So diagram 2 is the correct one, and it is our final solution.

Question on Circular seating arrangement

Seven friends, P, Q, R, S, T, U and V are sitting around a circular table. They are always facing towards the centre.

R is next to the left of U and V is second to the left of R.

P is sitting third to the left of T.

Q is between S and T.

 

Q1 Which statement is false?

A. P is fourth to the right of T.

B. U is to the immediate right of R.

C. U is third to the right of S.

D. Q is to the immediate left of S.

Ans: C) (look at the diagram and explanation below for clarity)

Q2 Which statement is false?

A. R is fourth to the right of T.

B. P is to the immediate right of V.

C. S is second to the left of T.

D. Q is second to the right of V.

Ans: A) (look at the diagram and explanation below for clarity)

Explanation:

List of statements:

  1. R is next to the left of U, and V is second to the left of R.
  2. P is sitting third to the left of T.
  3. Q is between S and T.

With the help of statement 1, we can start drawing the diagram, R is seated to the left of U and V is seated second to the left of R.

 

The next statement says that P is sitting third to the left of T, but this is non-specific information. We have to figure out where we can put P and T. The following are the four possibilities for T’s position, but the first two are invalid as there is no vacant place for P to the seat. In the last two possibilities, the position of T and P both seem to be correct.

 

The next statement says that Q is between S and T.

So diagram 4 also becomes invalid as there is no vacant place to put Q.

 

So the final correct circular arrangement is,

Question on Square /Rectangular seating arrangement

Eight people J, K, L, M, N, O, P and Q, are sitting around a square table. Four people are seated at the corners of the table while the other four are sitting in the middle position of each of the four sides. All are facing towards the center. Neither J nor O is an immediate neighbour of M. L is sitting fourth to the left of O. N is not sitting in the middle of any of the sides. J is sitting second to the left of O. J is not sitting in the middle of any sides. M is sitting in the middle of one of the sides. Only one person is sitting between K, and M. P is not an immediate neighbour of O. 

Explanation:

The given statements are:

  1. Neither J nor O is an immediate neighbour of M.
  2. L is sitting fourth to the left of O. 
  3. N is not sitting in the middle of any of the sides.
  4. J is sitting second to the left of O
  5. J is not sitting in the middle of any of the sides. 
  6. M is sitting in the middle of one of the sides.
  7. Only one person is sitting between K and M. 
  8. P is not an immediate neighbour of O. 

Let us start to draw the diagram. According to the problem everyone is facing towards the center.

 

We cannot deduce anything from statement 1 as we are not sure about the position of M.

Let's look at statement 2; according to it, there can be two possible positions of O and L. In the first possibility, O  and L can be seated at corners, and in the second possibility, O and P can be seated at middle positions.

 

Now let's look for some more statements related to the information that you just used. (tip no. 2)

We can see statement 4 is related to O. It says O is sitting second to the right of J. But we also see that statement 5 says J cannot be seated in the middle of one of the sides, so diagram 1 is not valid, and we discard diagram 1.

 

Now there is only one vacant corner left, and we can easily guess that N will be seated here. (see statement 3)

 

Let us now use all the remaining statements to fill up all the seats. According to statements 1 and 6, M can be also placed in the following position.

 

According to statement 8, there is only one possible way for P to be seated,

Following statement 7, this is the only way K can be seated as there has to be exactly 1 element between K and M.

 

There is only one place left to fill up now, so Q will be seated in that position. This is our final answer,

Question on Complex seating arrangement

Amit, Bharati, Cheryl, Deepak, and Eric are sitting in a restaurant, wearing different coloured caps: white, green, red, blue, and yellow. They are eating five different snacks: burgers, pastries, ice cream, sandwiches, and pizza. Cheryl is eating sandwiches. The person wearing a red cap is eating pastries. Eric is eating pizza but is not wearing a green cap. Amit does not eat ice cream. Bharati is wearing a yellow cap, and Amit is wearing a blue cap. 

Q1 Who is eating ice cream?

A. Amit

B. Bharati

C. Cheryl

D. Deepak

E. Eric

Ans: B) 

Q2 What is the color of Eric’s cap?

A. Blue

B. Red

C. Green

D. White

E. Yellow

Ans: D)

Explanation:

For solving this problem, we will create a table as follows,

Let us fill up the table with the given specific information,

The person wearing a red cap is eating pastries, as we cannot match any other person having the color of cap as red and pastry as food. Deepak seems to be the right fit.

It is known that Eric is not wearing a green cap, so it is implied that Cheryl is wearing the green cap.

As Amit is not eating ice cream, that leaves us with only one possibility that Bharati is eating ice cream.

Once that’s done, we can fill up the blank cells, and our final solution should look something like this,

Frequently asked questions

What are the different types of Seating Arrangements?

Ans: There are five types of seating arrangements:

  • Linear seating arrangement
  • Double row seating arrangement
  • Circular seating arrangement
  • Square / Rectangular seating arrangement
  • Complex seating arrangement

Key Takeaways

To summarize this blog, we went through the different seating arrangement problems, starting from linear, double row to complex. We also learned about some unique tricks to help you ace seating arrangement questions. We also went through one question about each type of arrangement.

We hope you have understood how to solve seating arrangement problems by the end of this blog. Happy Learning Ninja!
 

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