A simulation of two solutions to the "prisoner and two switches" problem (http://www.braingle.com/brainteasers/18012/prisoners-and-2-switches-scenario-a.html)

prisoner_problem_protocol.rb

class Leader
  attr_reader :count
  attr_reader :actually_visited

  def initialize
    @count = 1
    @actually_visited = false
  end

  def respond_to_state(s)
    @actually_visited = true
    case s
    when '00' then '01'
    when '01' then '00'
    when '10' then @count += 1 and '00'
    when '11' then @count += 1 and '01'
    end
  end

  def respond_to_state_emma(s)
    @actually_visited = true
    case s
    when '00' then '01'
    when '01' then '00'
    when '10' then @count += 1 and '00'
    when '11' then @count += 2 and '01'
    end
  end
end

class Prisoner
  attr_reader :actually_visited

  def initialize
    @visited = 0
    @actually_visited = false
  end

  def respond_to_state(s)
    @actually_visited = true

    if @visited == 0
      case s
      when '00' then @visited = 1 and '10'
      when '01' then @visited = 1 and '11'
      when '10' then '11'
      when '11' then '10'
      end
    else
      case s
      when '00' then '01'
      when '01' then '00'
      when '10' then '11'
      when '11' then '10'
      end
    end
  end

  def respond_to_state_emma(s)
    @actually_visited = true

    if @visited < 1
      case s
      when '00' then @visited += 1 and '10'
      when '01' then '00'
      when '10' then @visited += 1 and '11'
      when '11' then @visited -= 1 and '10'
      end
    else
      case s
      when '00' then '01'
      when '01' then '00'
      when '10' then @visited -= 1 and '00'
      when '11' then @visited -= 1 and '10'
      end
    end
  end
end

def run_problem(n, emma=false)
  # initialize everything
  leader = Leader.new
  prisoners = [leader]
  (n-1).times do
    prisoners << Prisoner.new
  end
  steps = 0
  state = '00'

  # run the algorithm
  until leader.count >= n
    steps += 1
    prisoner = prisoners.sample
    if emma
      state = prisoner.respond_to_state_emma(state)
    else
      state = prisoner.respond_to_state(state)
    end
  end

  # make sure we didn't fail
  if prisoners.any? {|p| !p.actually_visited }
    raise "BAD!"
  end

  # return number of steps
  steps
end

n_prisoners = 100
iterations = 100
norm_results = iterations.times.map { run_problem(n_prisoners, false) }
emma_results = iterations.times.map { run_problem(n_prisoners, true) }

puts "For n = #{n_prisoners} prisoners:"
puts "Emma's Average: #{emma_results.inject(0.0){ |sum, el| sum + el }.to_f / iterations}"
puts "Regular Average: #{norm_results.inject(0.0){ |sum, el| sum + el }.to_f / iterations}"