Hostel Room Allocation: Solving Seniority-Based Room Assignments

This problem involves a logical deduction process to determine room assignments in a hostel based on specific seniority and preference rules. We need to meticulously follow each rule for every student, in order of their seniority, to trace the path of room allocations and displacements.

Room Allocation Rules Explained

The core principles governing the hostel room allocation are as follows:

• Seniority Order: Students are allotted rooms strictly in order of their seniority, from the highest (1) to the lowest (4).
• Preferred Room Movement: If a student already has a room but finds a room in their preferred list available (or occupied by a lower seniority student), they will move to that preferred room.
• Preference Priority: The preferences of lower-ranked applicants (those with higher seniority numbers) are disregarded during the allocation process for higher-ranked students. This means a higher seniority student can displace a lower seniority student from their current room if it's on the higher seniority student's preference list.

Initial Room Occupancy Data

Let's begin by listing the given data for students, their seniority, current rooms, and room preference lists. This table helps us understand the starting configuration of the hostel rooms.

From the initial data, we can infer the starting occupancy of rooms P, Q, R, and S:

• Room P: Occupied by Amar
• Room Q: Occupied by Anthony
• Room R: Vacant (no student is initially listed as staying in room R)
• Room S: Occupied by Ajit

Step-by-Step Room Allocation by Seniority

Now, let's process the room allocations for each student, strictly following the seniority order from highest (1) to lowest (4).

Amar's Room Allocation (Seniority 1)

• Amar's Status: Amar is currently in Room P. His preference list is R, S, Q.
• As the most senior student, Amar checks his preferred rooms.
• Checks R: Room R is currently vacant. Amar successfully moves from Room P to Room R.
• Impact: Room P becomes vacant. Amar now occupies Room R.
• Room Status After Amar's Move:
  • Room P: Vacant
  • Room Q: Anthony
  • Room R: Amar
  • Room S: Ajit

Akbar's Room Allocation (Seniority 2)

• Akbar's Status: Akbar does not have a current room. His preference list is R, S.
• Akbar needs a room and evaluates his preferences.
• Checks R: Room R is occupied by Amar (Seniority 1). Since Amar has higher seniority than Akbar, Akbar cannot take Room R.
• Checks S: Room S is occupied by Ajit (Seniority 4). Since Akbar (Seniority 2) has higher seniority than Ajit (Seniority 4), Akbar can displace Ajit from Room S. Akbar moves into Room S.
• Impact: Room S becomes vacant. Ajit is displaced and is now without a room. Akbar now occupies Room S.
• Room Status After Akbar's Move:
  • Room P: Vacant
  • Room Q: Anthony
  • Room R: Amar
  • Room S: Akbar
  • Ajit is now without a room.

Anthony's Room Allocation (Seniority 3)

• Anthony's Status: Anthony is currently in Room Q. His preference list is P.
• Anthony checks his preferences.
• Checks P: Room P is currently vacant. Anthony moves from Room Q to Room P.
• Impact: Room Q becomes vacant. Anthony now occupies Room P.
• Room Status After Anthony's Move:
  • Room P: Anthony
  • Room Q: Vacant
  • Room R: Amar
  • Room S: Akbar
  • Ajit is still without a room.

Ajit's Room Allocation (Seniority 4)

• Ajit's Status: Ajit was displaced from Room S by Akbar and is currently without a room. His preference list is Q, P, R.
• Ajit is the last student to be allocated a room and checks his preferences in order.
• Checks Q: Room Q is currently vacant. Ajit successfully moves into Room Q.
• Impact: Ajit now occupies Room Q.
• Room Status After Ajit's Move:
  • Room P: Anthony
  • Room Q: Ajit
  • Room R: Amar
  • Room S: Akbar

Final Room Allocation Summary

After processing all students according to their seniority and preferences, the final room assignments are as follows:

Ajit's Final Room Assignment

Based on the detailed step-by-step allocation process, Ajit will stay in Room Q.