Quick and gross sketch to play out logic puzzle about probability of last pax on plane getting their seat if a random pax goes "rogue" and takes seat not assigned to them

mit_tech_review_logic_puzzle_plane_boarding.py

import random

class Passenger:
    """Passenger with seating ticket."""
    def __init__(self, seat: int):
        self.seat_assigned = seat
        self.seat_taken = None
        self.is_rogue = False  # if rogue, pax will sit in wrong seat
        
    def make_rogue(self):
        self.is_rogue = True
    
    def take_seat(self, seat_num: int):
        self.seat_taken = seat_num
        
        # we can check later if correct seat was taken for what portion of riders
        self.took_correct_seat = self.seat_assigned == self.seat_taken


class Plane:
    """Class for plane object."""
    def __init__(self, seat_count: int):
        # initally no one is seated anywhere, plane empty
        self.seats = [None] * seat_count
    
    def seat_pax(self, pax: Passenger):
        """Check if seat is available for passenger and seat else seat elsewhere."""
        if self.seats[pax.seat_assigned] is None and not pax.is_rogue:
            # this means the seat is not yet taken so assign the pax to that seat
            seat_num = pax.seat_assigned
        else:
            # otherwise we have rogue pax that took the wrong seat
            remaining_seats = [i for i, s in enumerate(self.seats) if s is None]
            random.shuffle(remaining_seats)
            
            # grab a random next seat
            seat_num = remaining_seats[0]
            if pax.is_rogue and pax.seat_assigned == seat_num:
                seat_num = remaining_seats[1]

        # finally seat pax with secured open seat
        pax.take_seat(seat_num)
        self.seats[seat_num] = pax


def simulate(seat_count: int) -> bool:
    """Run simulation and return result of seating assing of last pax."""
    # create the plane and passengers
    plane = Plane(seat_count)
    passengers = [Passenger(x) for x in range(seat_count)]

    # the first passenger is the rule breaker
    passengers[0].make_rogue()

    # start seating process
    [plane.seat_pax(p) for p in passengers]

    last_pax = passengers[-1]
    last_pax_got_assigned_seat = last_pax.seat_assigned ==  last_pax.seat_taken
    return last_pax_got_assigned_seat


if __name__ == "__main__":
  results = [simulate(100) for _ in range(5000)]
  pct_last_pass_success = float(sum([1 for r in results if r]))/len(results)
  print(f"Percent of times last passenger got their seat: {pct_last_pass_success}")

Results distribution will normalize around 50% of the time passenger will not get their assigned seat.