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Circular Arrangement

Problems on circular arrangement involve seating positions of people around a table. The shape of the table could be a square, a rectangle, a circle, a hexagon, etc.

These types of problems will have statements such as persons sitting opposite to each other, a particular person sitting to the right or left of another person, etc. After interpreting and analysing the statements, we should draw the seating diagram, duly complying with all the conditions.

If four persons are sitting around a square, rectangular or circular table, the positions can be marked as follows:
 
Description: 73505.png

If six persons are sitting around a circular or rectangular table, their positions can be marked as under:
 
Description: 73514.png

If eight persons are sitting around a square table—four persons at the middle of the sides and four persons at the corners—the positions can be shown as:
 
Description: 73523.png
 
Whenever the phrase ‘A is sitting one seat away from B’ is used, students should understand that there is one person between A and B. It is as good as saying that A is sitting in the second seat from B. Similarly, if A is sitting two seats away from B, it implies that there are two persons between A and B. This is same as saying that A is sitting in the third seat from B.
 

Example

Directions:
A, B, C, D and E sit around a circular table and play ‘Rummy’. A is sitting one seat away to the left of C, and B is sitting one seat away to the right of C.

  1. If D sits between B and C, who sits to the immediate right of A?
    1. E
    2. D
    3. B
    4. C
    5. Cannot be determined
  2. Which of the following cannot be the correct seating arrangement of these persons either in clockwise or anticlockwise direction?
    1. A B C D E
    2. A D C E B
    3. A B D C E
    4. A E C D B
    5. None of these
  3. If D is not sitting next to B, who is sitting between B and D?
    1. C
    2. A
    3. E
    4. Cannot be determined
    5. None of these
  4. If another person ‘F’ joins the game, but does not sit next to C, whereas the others sit in their earlier positions, then which of the following statement is correct?
    1. F sits to the immediate right of D.
    2. F sits to the immediate left of A.
    3. F sits to the immediate left of E.
    4. Either (1) or (2).
    5. Either (1) or (2) or (3).

Solution

Based on the conditions given in the statements, A sits one seat away to the left of C and B sits one seat away to the right of C. We can draw their positions as shown in the adjacent figure.

 

Description: 73872.png
 

Now, the questions can be answered as follows:

  1. If D sits between B and C, then the arrangement will be as shown in the adjacent figure. So, E is sitting to the immediate right of A.
     
    Description: 73594.png
     
    Answer: (1) 
  2. Try each of the given options and find out which option fails to indicate a correct seating arrangement.
     
    Description: 73610.png
     
    Answer: (1) 
  3. If D is not sitting next to B, then the arrangement will be as shown in the adjacent diagram.
     
    Description: 73629.png
     
    Now, A is between B and D.
     
    Answer: (2) 
  4. On the basis of the positions of A, B, C, D and E in the diagram, F can be positioned between A and B. If F sits in any other positions, original conditions get violated.
     
    Description: 73650.png
     
    Answer: (2)




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