Seating Arrangements (Circular and Linear)

If you are preparing for any competitive exams, you must have come around some questions where you have to arrange people in a manner to satisfy every given condition. These types of problems are called sitting arrangement problems or reasonings. Generally, people find this topic tricky and lengthy.

Here we are going to discuss the key concepts, types, terminologies examples, and tricks and tips to solve problems related to seating arrangements, linear seating arrangements, and circular seating arrangements.

Linear Seating Arrangement

A linear seating arrangement is a simple seating arrangement in which people or objects are arranged in a straight line. Problem-related to linear seating arrangement includes questions related to the specific position, position concerning one another in single or multiple rows based on the conditions given.

Let’s have a view over different types of linear Seating arrangements

Types Of Linear Seating Arrangements

• Single Row Unidirectional:

In this type of linear seating arrangement, people or objects are arranged in a single row with everyone facing the same direction.

• Single Row Bidirectional:

In this type of seating arrangement, people or objects are arranged in a single row but with everyone facing 2 different directions.

• Dual Row:

In this type of seating arrangement, People or objects are arranged in two different rows.

Tips And Tricks To Solve Questions Based On Linear Seating Arrangement.

1. In an arrangement, if P is said to be three people away from Q. That means 2 (3-1) people are seated between them.
2. If P is second to the left of Q -> P_Q
3. If P is second to the right of Q -> Q_P
4. If P is 2 places right or left to Q -> P_Q
5. If P is 2 places away from Q -> P/Q_ _ Q/P
6. If there are 2 people between P and Q -> P_ _Q

Note: Practice as much as you can so that you can master questions related to linear seating arrangements.

Examples Based On Linear Seating Arrangement

Example1. 5 people are standing in a queue at a bus stop P, Q, R, S, and T. P is right of Q, R is right of T, and P is left to T. Q is right to S. Now, who is in the middle?

Solution-> 

If we arrange P, Q, R, S, and T according to the question we get

QP, TR, PT, and SQ

On arranging this we get the order

S, Q, P, T, and R

We have P in the middle.

Example2. A, B, C, D, E, F, and G are sitting in a row facing East. F is to the right of E. E is 4th at the right of G. C is in between B and D. Person third to the left of D has no one at the other side. Who are the Neighbours of B? 

Solution-> 

If we arrange A, B, C, D, E, F, and G according to the question we get the following arrangement. 

G, B, C, D, E, F, and A

C and G are the neighbors of B.

Circular Seating Arrangement

Circular Seating Arrangement is a special Seating Arrangement in which People or objects are placed in a circular form (closed circular loop). This also includes problems related to specific positions and positions to one another. Let’s go through different types of circular Seating Arrangements.

Types of Circular Seating Arrangement

• Circular Unidirectional:

In this type of Circular seating arrangement people or objects are arranged in the circular closed loop with everyone facing in the same direction. The direction could be inside or even outside the circular arrangement.

• Circular Bidirectional:

In this type of circular seating arrangement people or objects are arranged in a circular closed loop with people facing in two different directions. Some of them are facing inside while others are facing outside the circular arrangement. 

Tips And Ticks To solve Questions Based On Circular Seating Arrangement.

1. Circular Arrangement could be of either direction, Clockwise and Anticlockwise direction.
2. Count the no. of people and draw a circle. Now, mark lines on the circles equal to the number of people.
3. In an arrangement, if P is said to be three people away from Q. That means 2 (3-1) people are seated between them.
4. If P is second to the left of Q -> P_Q
5. If P is second to the right of Q -> Q_P
6. If P is 2 places right or left to Q -> P_Q
7. If P is 2 places away from Q -> P/Q_ _ Q/P
8. If there are 2 people between P and Q -> P_ _Q

Note: Practice as much as you can so that you can master questions related to linear seating arrangements.

Examples Based On Circular Seating Arrangement

Example1. In a circular arrangement four girls A, B, C, and  D, and four boys E, F, G, and H are seated facing inside. In this arrangement, no one of the same gender is sitting together. G and E have C in between them facing D. F is between D and A facing G. And B is the immediate left of H. Who is sitting left of A?

Solution->

If we arrange A, B, C, D, E, F, G, and H according to the conditions given in the question we get the following arrangement

B, H, C, E, A, F, D, G, and B clockwise.

Now, we can see that F is sitting to the left of A.

Example2. Eight friends Ama, Bob, Cab, Eva, Dev, Fib, Gom, and Ham are sitting in a circular arrangement. They are not necessarily sitting in the same arrangement but are facing towards the center of the table. Eva Is third to the left of Gom. Bob and cab are neighbors. Ama is sitting opposite Fid. Dev is sitting next to Gom. Two people are sitting between Eva and Fib. Bob and Ham are sitting opposite each other. Who is sitting immediately right to Eva?

Solution-> 

According to the question,

1. Eva Is third to the left of Gom. 
2. Bob and cab are neighbors. 
3. Ama is sitting opposite Fid. 
4. Dev is sitting next to Gom. 
5. Two people sitting between Eva and Fib. 
6. Bob and Ham are sitting opposite each other.

Hence, the arrangement is in the order:

Ama, Eva, Cab, Bob, Fib, Dev, Gom, and Ham are in the clockwise direction. 

Now, Ama is sitting right to Eva.

Cluster Seating Arrangement

Cluster seating arrangement also known as rectangular seating arrangement is a seating arrangement in which people or objects are seated around a rectangular table, and always face inside. It is almost similar to the circular arrangement but around a rectangular table.

Tips And Ticks To solve Questions Based On Cluster Seating Arrangement.

1. In an arrangement, if P is said to be three people away from Q. That means 2 (3-1) people are seated between them.
2. If P is second to the left of Q -> P_Q
3. If P is second to the right of Q -> Q_P
4. If P is 2 places right or left to Q -> P_Q
5. If P is 2 places away from Q -> P/Q_ _ Q/P
6. If there are 2 people between P and Q -> P_ _Q

Note: Practice as much as you can so that you can master questions related to linear seating arrangements.

Examples Based On Cluster Seating Arrangement

Example1. Eight girls A, B, C, D, E, F, G, and H are sitting around a square table facing the center. A sits 6th to the left of B who sits third to the right of F. E sits second to the left of F. G sits between A and B she sits immediately left to F. Who is immediately left to do who sits second to the left of D?

Solution->

According to the above information, 

The sitting arrangement would be A, G, B, H, D, F, C, and E in the clockwise direction. Hence C is sitting left second to the left of D.