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Difficulty: EasySeating Arrangement

Four delegates—David, Emma, Felix, and Grace—are sitting on a panel in a straight row facing the audience. There are four chairs numbered 1 to 4 from left to right. Arrange their seating positions from seat 1 (far left) to seat 4 (far right) based on the following conditions:

1. Felix is sitting in seat number 4, at the extreme right end.
2. David is sitting immediately to the right of Emma.
3. Grace is not sitting next to David.

  1. 1Grace
  2. 2Emma
  3. 3David
  4. 4Felix

Answer

The correct seating order from left to right is Grace (seat 1), Emma (seat 2), David (seat 3), and Felix (seat 4).
Based on the constraints, Felix is firmly in the 4th position. The pair (Emma, David) must occupy adjacent seats. Placing them in seats 1 and 2 leaves seat 3 for Grace, which illegally positions her next to David. Therefore, the (Emma, David) pair must go to seats 2 and 3, leaving seat 1 for Grace, which legally separates Grace and David.

Step-by-Step Solution

1
Assign Felix's position.
Felix is in seat 4.
The first condition explicitly states that Felix is sitting at the extreme right end (seat 4).
2
Determine the relative positioning of David and Emma.
Emma sits to the left of David (Emma, then David).
The second condition states David is immediately to the right of Emma.
3
Place Emma, David, and Grace into the remaining seats (1, 2, and 3).
Grace takes seat 1, Emma takes seat 2, and David takes seat 3.
If Emma and David took seats 1 and 2, Grace would be forced into seat 3, making her a neighbor to David. This violates the third condition. Therefore, Emma and David must take seats 2 and 3, leaving seat 1 for Grace.

Key Concept

Linear Seating Arrangement
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Topics

Seating Arrangement

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