Overview of Linear Arrangements

Linear Arrangements

A linear arrangement is a form of seating arrangement where people or things must be arranged in a straight line. In linear arrangement reasoning questions, candidates must place persons in a row or many rows based on the stated requirements. Based on the information provided, examinees must determine the actual position of items and their relative positions to one another. 

Different competitive exams will examine your logical thinking and problem-solving skills through logical reasoning and verbal reasoning questions. Linear arrangement reasoning questions are commonly asked in job interviews. While preparing for your examination or interview, it is critical to be familiar with seating arrangement questions and solutions. So let us discuss a seating or linear arrangement and its types and learn from examples and responses.

Types of Linear Arrangements

A linear arrangement is the process of arranging items or groups in a predetermined or logical order. There are several types of linear arrangements:

Arrangement in a line 

People or things sitting in a row horizontally, diagonally, or vertically make a linear seating arrangement. For example, students standing in a prayer hall or passengers seated on a train are two real-life instances of linear arrangements in a line. 

Single Row unidirectional 

In this configuration, all individuals are arranged in a single row facing the same way.

Single Row Bidirectional 

In this arrangement, individuals or items are arranged in a single row facing opposite directions.

Dual Row 

In this configuration, people are arranged in two separate rows.

Arrangement in a Circle

People or things are arranged in a circular pattern in a circular arrangement. Real-life examples of circular arrangements include a family eating meals around a circular table or things arranged in a circle. This can be of two types.

• Circular facing the centre: Everyone seated at a circular table faces the circle’s centre. Candidates seated in a circle during a group discussion are examples of a circle facing the centre.
• Everyone who sits around a circular table or in a round fashion faces outwards.

Arrangement in Polygons

Polygons are closed figures with three or more sides. People or objects sit around a polygonal form in this seating configuration. Triangles, rectangular, hexagonal, pentagonal, and octagonal forms are all possible.

• Triangle arrangement: People or things are arranged in a triangle pattern or around a triangular table.
• Arrangement in square: People or things are arranged around a square surface or table.

Complex Arrangement

Each object or person in a linear arrangement has just one property connected to their placement, whereas each thing in a complex arrangement has several qualities. 

• Table creation entails tabulating data based on logical requirements and placing each object in a specific column and row.
• Matric tabulation: In matric tabulation, you put things as a matrix using special letters and symbols.

Steps to Answer Seating Arrangement Questions

To answer seating arrangement questions, use the following steps:

Recognise the Type of Inquiry

Read the question and determine if the layout is linear, circular, or polygonal. If the problem is circular, create a circle to seat things or people around it. Draw a straight line and fill the slots to seat everyone in the question if it is a linear layout question.

Obtain Information

Gathering and writing down all relevant information is the first step in answering seating arrangement questions in an interview. To answer the problem, use the direct information provided in the question. There is some direct information in all seating arrangement inquiries.

Employ Indirect Information

Look for a probable relationship between additional pieces of information once you have filled in the direct information. For example, in a linear arrangement problem, knowing that person A is not seated to the left of person B suggests that person A is seated to the right of person B. Hence, in order to answer such queries, seek indirect information.

Fill the Available Seats

The next stage is to fill the seats that have been assigned based on direct and indirect information. For example, if person C is seated between person A and person B in a linear configuration, there are two options: ACB or BCA. Thus, create two separate linear layouts depending on the information in the question. Assume any arrangements and organise other persons accordingly to solve such difficulties. If you successfully solved the entire issue, the first arrangement you assumed is accurate; otherwise, the other arrangement is correct.

Example of a Linear Arrangement Reasoning Problem

The letters J, K, L, M, N, O, P, Q, and R are arranged in a straight line. A few are oriented north, while just three are oriented south. O’s neighbour is P, who is seated eighth from the right end. R is not M’s neighbour. J is seated to the third left of O. O is seated fifth, to the right of M. N’s extreme right neighbour is M. K is seated fifth, to the right of Q. N is seated fifth from the left side of the starting line.

Q. How many people are sitting between J and L?

a) 1, b) 2, c) 3, d) 4, e) 5

Ans: (c)

Q. Who is sitting at the extreme end?

a) L, b) M, c) Q, d) R, e) N

Ans: (e)

Conclusion 

To solve linear arrangement problems, you must concentrate on sequences of the offered questions. First, choose whether the layout is linear, square, polygonal, or round. Obtain knowledge and utilise the indirect information provided by the question to solve it correctly and in the shortest duration.