Seating Arrangement Puzzle Explained

This solution explains how to solve a logic puzzle about seven people (A, B, C, D, E, F, G) sitting in a row facing north. We will determine the exact seating arrangement based on the given clues to find out how many people are sitting to the right of person A.

Constraints Analysis Seating Arrangement

First, let's list and understand all the conditions given in the problem:

• There are 7 people: A, B, C, D, E, F, G.
• They are sitting in a row facing North.
• Condition 1: Exactly two people sit between D and C. (This implies the pattern is D _ _ C or C _ _ D).
• Condition 2: Only G sits to the right of E. (This implies they sit together in the order E G).
• Condition 3: Exactly one person sits between C and E. (This implies the pattern is C _ E or E _ C).
• Condition 4: A sits somewhere to the right of F, and A sits somewhere to the left of B. (The relative order must be F ... A ... B).

Arrangement Derivation Step-by-Step

Let's combine the constraints to find the seating order. We represent the 7 positions as 1 2 3 4 5 6 7 (from left to right, as they face North).

We can combine Condition 1 (D _ _ C) and Condition 3 (C _ E). If D is to the left of C, and C is to the left of E (with one person between them), the combined structure looks like D _ _ C _ E. This sequence uses 6 positions.

Now, let's incorporate Condition 2 (E G). Since G must sit immediately to the right of E, the sequence extends to D _ _ C _ E G. This sequence perfectly accommodates all 7 people.

The structure based on these combined conditions is: [D] [_] [_] [C] [_] [E] [G].

The people remaining to be placed are F, A, and B. We need to place them in the empty seats (positions 2, 3, and 5) following Condition 4 (F ... A ... B).

Fitting F, A, B into seats 2, 3, and 5 while maintaining the order F...A...B requires:

• F in seat 2
• A in seat 3
• B in seat 5

This leads to the final seating arrangement:

D F A C B E G

Let's verify this arrangement against all the initial conditions:

• D _ _ C: The arrangement is D(1) F(2) A(3) C(4). F and A (2 people) are between D and C. Condition met.
• E G: The arrangement is E(6) G(7). G is immediately right of E. Condition met.
• C _ E: The arrangement is C(4) B(5) E(6). B (1 person) is between C and E. Condition met.
• F ... A ... B: The arrangement is F(2) A(3) B(5). A is to the right of F and to the left of B. Condition met.

Since all conditions are satisfied, this is the correct arrangement.

People Right of A Calculation

In the determined arrangement, D F A C B E G:

• Person A is located in the 3rd position from the left.
• The positions to the right of A are the 4th, 5th, 6th, and 7th positions.
• The people sitting in these positions are C, B, E, and G respectively.
• Counting these individuals, we find there are exactly 4 people sitting to the right of A.