Puzzle – Sitting Arrangement

Sitting Arrangement or Seating Arrangement is a popular puzzle that involves determining the position of a person in a group of persons/objects who are seated in a row or in a circle on the basis of the given clues. 
The main objective of this puzzle is either to determine the complete sitting arrangement of people or the position of a particular person in the sitting arrangement which obeys the given clues. The clues involve information about the relationships between the people or their positions relative to each other. One requires careful attention to the clues and logical aptitude to solve this puzzle.

This puzzle can be classified on the basis of the types of arrangements, in which the group of people is arranged. Different possible seating arrangements are listed as follows:

• Linear Arrangement
• Triangular arrangement
• Rectangular/Square Arrangement
• Pentagonal arrangement
• Hexagonal arrangement
• Circular Arrangement
• A combination of above

The aim of each type of puzzle, listed above, remains the same, i.e. to arrange the group of persons/objects satisfying certain conditions. The way to solve these puzzles would be clear when you walk through the solutions of the example problems discussed hereafter.

List of Exams where it is asked:

The “Sitting Arrangement” puzzle can be an appropriate tool for testing a candidate’s cognitive ability, numerical ability, and abstract reasoning. So, it is asked in various aptitude tests for entrance exams, placements, and government job exams. 

A few exams in which the puzzle is frequently asked are listed below:

• Bank PO/Clerk Exams
• SSC Exams (Staff Selection Commission)
• CAT Exam (Common Admission Test)
• GMAT Exam (Graduate Management Admission Test)
• UPSC (Union Public Service Commission) Exams
• CSAT (Civil Services Aptitude Test)
• CLAT Exam (Common Law Admission Test)

Apart from these competitive exams, the puzzle is also popular as a brain teaser in puzzle books and magazines.

Solved Examples:

Example 1:

In a queue at a ticket center, 7 persons named Alice, Bob, Charlie, David, Frank, James, and Nick are standing facing the west, not necessarily in the same order. The arrangement follows the following rules:

• Alice is next to the right of Nick.
• Nick is fourth to the right of Charlie.
• David is between James and Bob.
• Charlie who is third to the left of Bob is at one end.

Answer the following questions based on the arrangement described above.

Question 1: Who is between James and Bob?
Answer: David

Question 2: Who is 3rd to the right of David?
Answer: Alice

Solution: The basic approach to solving these puzzles should be, to try to build the arrangement from the given hints. For this puzzle let us assume first, we have 7 empty seats, and we will fill all these seats subsequently.

Initial Arrangement

From the fourth hint, we come to know that Charlie is at one of the ends. But in the second hint, we observe that there is someone right to him, so he must be at the left end of the queue. Now from the second and fourth hints, we come to know the positions of Charlie, Bob, and  Nick. The arrangement so far:

Arrangement after using the 2nd and 4th hint

From the first and third hints, the arrangement:

Final Arrangement

Thus, we derived the arrangement from the given hints. And, each question related to this arrangement can be easily answered hereafter.

Example2:

Answer the following questions related to the seating arrangement of 5 sportspersons namely A, B, C, D, and E sitting in a row for a press conference based on the following hints:

• D is to the right of B.
• E is between B and D.
• A is to the left of B and to the right of C.

Question 1: Who is in the middle of the row?
Answer: B

Question 2: Who is sitting at the immediate left of D?
Answer: E

Solution:
From the first and second hints, we come to know that our arrangement will surely include the ‘B-E-D’ sequence. Now, the third hint tells us that A is to the left of B, so our sequence would be of the ‘A-B-E-D’ type. Also, as A is to the right of C, we come to know that the arrangement would be:

Final Arrangement

As we derived the seating arrangement from the given hints, we can answer any question related to this seating arrangement.