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Seating Arrangement

The problems on seating arrangements deal with arranging a group of people/objects in a line, or around a circle, which subject to certain conditions given therein. If the arrangement consists of people/objects placed in a line, it is called as linear arrangement. If the people/objects are placed around a circular table, square table, hexagonal table, etc., it is called as circular arrangement.
The given information can be broadly classified into two categories:
Actual information: Information regarding the actual seating arrangement of the persons or objects is called actual information.
  1. A is sitting at one of the ends of a row.
  2. B is sitting next to A.

Useful secondary information: Information which does not directly deal with actual seating arrangement, but indirectly help us to understand the situation is called useful secondary information (USI).

  1. Six people are playing cards.
  2. Four people are sitting on a bench.

Actual information can be further classified into three subcategories as under:


Definite information or specific information: Information in which the position/place of any person or object is definitely stated is called definite information or specific information.

  1. B is sitting at the extreme left end of a bench in a park.
  2. D is sitting second from the right.

In the above statements, positions of B and D are clearly stated.


Comparative information: Information in which the exact place/position of any person or object is not definitely mentioned, but only a comparative position is given, is called comparative information.

  1. E is sitting next to B.
  2. A and D are sitting together.

In the above statements, the positions/places of E and B, or A and D, are not definitely known. We know only their comparative or relative positions.


Negative information: Information which denies a particular seating arrangement is called negative information.

  1. A is not sitting with B.
  2. C is not sitting at the end of the row.

Though the negative information does not provide any specific information about the seating arrangement, it gives us a clue to eliminate one or more of the possibilities.

To solve the problems on seating arrangements, we should first focus on the actual information keeping aside the useful secondary information (USI).
Following steps should be followed in order to solve the problems on seating arrangements.
  1. Draw a diagram of empty places. If the people are sitting in a row, draw a horizontal line. Otherwise, draw the diagram as per the specifications given in the problem.
  2. Using the entire definite information, fill up as many empty places as possible.
  3. Then examine the comparative information, negative information and USI, if any. After considering all the possibilities and without violating any of the conditions, complete the seating diagram.
Once the seating diagram is completed, it is very easy to answer the questions asked in the problem.
While choosing comparative information, we should be careful in giving priority to the given specific conditions. In addition, it should be noted that the left or right of a person in linear seating arrangement is same as the left or right of a person solving the problem.

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