Question

A, B, C and D are to be seated in a row. But C and D cannot be together. Also B cannot be at the third place. Which of the following must be false?

• A. A is at the first place
• B. A is at the second place
• C. A is at the third place
• D. A is at the fourth place

Hint:

In "must be false" logic puzzles, assume the option is true and try to force a valid arrangement. The moment you hit an unavoidable contradiction with the rules, you have found your answer.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This is a logical seating arrangement problem. We have 4 individuals (A, B, C, D) and 4 seats (1, 2, 3, 4). We must evaluate the given options against two strict constraints to find the one that creates an impossible scenario.
Constraints:
1. C and D cannot sit adjacent to each other.
2. B cannot occupy the 3rd seat (Seat 3 \( \neq \) B).


Step 2: Detailed Explanation:
Let's test each option to see if a valid seating arrangement can be formed:
Evaluating Option (A): A is at the first place
Arrangement so far: [A] [_] [_] [_]
Remaining people: B, C, D. Remaining seats: 2, 3, 4.
To satisfy Constraint 1 (C and D not together), they must be separated by at least one seat. The only way to place them in seats 2, 3, and 4 without them being adjacent is to place them in Seat 2 and Seat 4.
If C and D occupy Seats 2 and 4, then Seat 3 is the only one left for B.
However, Constraint 2 strictly states that B cannot be at the 3rd place.
This creates a forced contradiction. Therefore, A cannot be at the first place. This statement must be false.
Evaluating Option (B): A is at the second place (Verification)
Arrangement: [_] [A] [_] [_]
To keep C and D apart, they can sit at Seat 1 and Seat 3, or Seat 1 and Seat 4.
If C and D take 1 and 3, B is forced to Seat 4. Valid arrangements: [C, A, D, B] or [D, A, C, B].
Since a valid arrangement exists, this statement can be true.
Evaluating Option (C): A is at the third place (Verification)
Arrangement: [_] [_] [A] [_]
To keep C and D apart, they must sit at Seat 1 and Seat 4.
This leaves Seat 2 for B. Valid arrangements: [C, B, A, D] or [D, B, A, C].
Since a valid arrangement exists, this statement can be true.
Evaluating Option (D): A is at the fourth place (Verification)
Arrangement: [_] [_] [_] [A]
To keep C and D apart, they must sit at Seat 1 and Seat 3.
This leaves Seat 2 for B. Valid arrangements: [C, B, D, A] or [D, B, C, A].
Since a valid arrangement exists, this statement can be true.


Step 3: Final Answer:
The statement that must be false is "A is at the first place".