Startup Room Allocation Puzzle: Identifying Siblings

This problem requires identifying the sibling pair among five individuals (P, Q, R, S, T) based on specific room allocation rules within a startup.

Key Constraints and Deductions

• Individuals involved: P, Q, R, S, T.
• Number of rooms: 3.
• Number of siblings: Exactly 2.
• Rule 1: Siblings must occupy different rooms.
• Condition 1: S is a single child, hence cannot be one of the siblings.
• Condition 2: Q is a single child, hence cannot be one of the siblings.

Based on these conditions, the siblings must be selected from the remaining individuals: P, R, and T.

The possible sibling pairs are therefore:

• P and R
• P and T
• R and T

Evaluating Provided Options

The options given for the sibling pair are:

• 1. P and T
• 2. P and S
• 3. T and Q
• 4. T and R

Applying the deductions from the constraints:

• Option 2 (P and S) is eliminated because S cannot be a sibling.
• Option 3 (T and Q) is eliminated because Q cannot be a sibling.

This leaves Option 1 (P and T) and Option 4 (T and R) as the only potential correct answers, as both pairs consist of individuals from the set {P, R, T}.

Final Determination of Siblings

The problem implies a unique solution exists. We must select the pair for which a valid room allocation is possible, adhering to all rules. If P and T are the siblings, they must be in separate rooms.

Consider the allocation: Room 1 contains {P, R}, Room 2 contains {T, S}, and Room 3 contains {Q}.

• This allocation uses 3 rooms for the 5 people.
• P and T are in different rooms (Room 1 and Room 2, respectively), satisfying the sibling rule.
• S and Q are placed, and their status as single children does not prevent this allocation.

Since a valid allocation exists where P and T are siblings and adhere to all rules, this pair is the correct answer.