Assigned seats + missing ticket puzzle

I just came across this tweet and thought it would be fun to share here:

Josh Wolfe

@wolfejosh

PUZZLE:
100 people line up to take their seats in a 100💺theater

The 1st in line lost her 🎟
sits in a💺at random

Each remaining theatergoer sits in their assigned💺unless it's occupied & then sits in a random💺

What's the probability the last person in takes their assigned💺?

02:48 AM - 20 Jul 2018

It looks like some people in the Twitter replies have already come up with a solution, but I thought it would be a fun puzzle nonetheless!

Comments

[Martin-Alexander]

Here's my simulation in Ruby. I know that one million is overkill, Lol

Spoilers below ↓

class Threater
  def self.run(iterations = 1_000_000)
    last_person_got_seat = 0.0
    total_runs = 0.0

    iterations.times do |i|
      if i % 1000 == 0
        print("\rNº of iterations: #{i.to_s.ljust(iterations.to_s.length)}")
      end
      last_person_got_seat += 1 if new.last_person_got_seat
      total_runs += 1
    end

    last_person_got_seat / total_runs
  end

  def initialize(threater_size = 100)
    @seats = [nil] * threater_size
    @seats[random_seat] = 0 # 1st in line lost her 🎟

    (1...threater_size).to_a.each do |person_seat|
      seat_person(person_seat, person_seat)
    end
  end

  def last_person_got_seat
    @seats.last == 99
  end

  private

  def random_seat
    rand([e-mail])
  end

  def seat_person(seat, person)
    if @seats[seat]
      seat_person(random_seat, person)
    else
      @seats[seat] = person
    end
  end
end


result = Threater.run
puts "\nResult: #{result}%"

It's 50%, apparently!

[Priyansh Jain]

When the 100th person enters, the occupied seats are 99, so the seat is either his or it isn't. Hence 50%, matches with the twitter feed. Not sure if this approach is right though.