Understanding the Seating Arrangement Puzzle

We are given a seating arrangement puzzle involving seven people: A, B, C, D, E, F, and G. They are all sitting in a single row and facing the north direction. We need to determine the seating position of each person based on the given clues to find out who is sitting third from the right end.

Step-by-Step Solution Derivation

Let's analyze the clues and deduce the seating arrangement:

• Clue 1: F sits on the extreme left end of the row. Since there are 7 positions, F is at position 1. Arrangement: F _ _ _ _ _ _
• Clue 2: There are three persons between F and B. Since F is at position 1, B must be at position 5 (F _ _ _ B). Arrangement: F _ _ _ B _ _
• Clue 3: E has equal number of persons to his left and right side. This means E must be exactly in the middle of the row. In a row of 7 people, the middle position is the 4th position. Arrangement: F _ _ E B _ _
• Clue 4: G sits second from one of the ends. This means G can be either at position 2 (second from the left) or position 6 (second from the right). Let's consider both possibilities.
  • Possibility 1: G is second from the left (position 2). Arrangement: F G _ E B _ _ The remaining positions are 3, 6, and 7. The remaining people are A, C, and D. We know that A sits immediate right of C (C A). If C is at position 3, A must be at position 4. But position 4 is occupied by E. So, C cannot be at position 3. If C is at position 6, A must be at position 7. But A cannot sit at the corner (position 7). So, C cannot be at position 6. This possibility leads to a contradiction, so G cannot be at position 2.
  • Possibility 2: G is second from the right (position 6). Arrangement: F _ _ E B G _ The remaining positions are 2, 3, and 7. The remaining people are A, C, and D. We need to place the pair C A. A does not sit at the corner. If C is at position 2, A must be at position 3. This fits the condition `C A` and A is not at a corner. Arrangement: F C A E B G _ The last remaining person is D, who must sit at the last position (position 7). Arrangement: F C A E B G D Let's verify the condition "A does not sit at the corner". A is at position 3, which is not a corner. This arrangement is valid.
• Final Arrangement Confirmation: The final seating arrangement from left to right is: F, C, A, E, B, G, D. Positions: 1, 2, 3, 4, 5, 6, 7. Let's check all conditions:
  • 7 people, facing north: Yes.
  • G second from end: G is at 6 (second from right). Yes.
  • E in the middle: E is at 4. Yes.
  • F on extreme left: F is at 1. Yes.
  • 3 people between F and B: F(1) ... B(5). Yes.
  • A immediate right of C: C(2) A(3). Yes.
  • A not at corner: A is at 3. Yes.
  All conditions are satisfied.
• Finding the person third from the right end: The row arrangement is F C A E B G D. The positions from the right are:
  • 1st from right: D (Position 7)
  • 2nd from right: G (Position 6)
  • 3rd from right: B (Position 5)

Therefore, B is sitting third from the right end.