A simulation of the ten letters, ten envelopes problem.

TenLettersTenEnvelopes.rb

# Original puzzle: A secretary receives 10 letters along with 10 addressed 
# envelopes to be sent out. She accidentally drops the all the letters and 
# envelopes and mixes them all up. So, she decides to put each of the 10 
# letters randomly into one of the 10 addressed envelopes and mail them out. 
# What is the probability that at least one letter arrives at the correct 
# destination?

# Gets a hash that represents the envelopes containing their randomly placed
# letter. Both envelope and letter are represented by a number. If the key and
# the value of each item in the hash are the same, that is a correct
# combination.
def get_envelopes
  letters = [1,2,3,4,5,6,7,8,9,10]
  envelopes = {1 => nil, 2 => nil, 3 => nil, 4 => nil, 5 => nil, 6=> nil, 
    7 => nil, 8 => nil, 9=> nil, 10 => nil}
  
  10.times do |n|
    index = rand(letters.count)
    envelopes[n+1] = letters[index]
    letters.delete_at(index)
  end
  
  return envelopes
end

# Takes a hash and compares the key and the value. If they match, it increments
# a count. When the hash has been looped over, the count is returned.
def count_correct_envelopes(envelopes)
  count = 0
  envelopes.each do |key, value|
    if key == value then 
      count += 1
    end
  end
  return count
end

# Number of simulations to run.
simulations = 50000

# A hash that will eventually contain the count for how many envelopes
# contained the correct letter in them.
correct_envelopes = {0 => 0, 1 => 0, 2 => 0, 3 => 0, 4 => 0, 5 => 0, 6=> 0, 
  7 => 0, 8 => 0, 9=> 0, 10 => 0}
  
# Run the simulation, count how many envelopes were correct each time
simulations.times do
  correct_envelopes[count_correct_envelopes(get_envelopes)] +=1
end

# Print the results.
at_least_one_correct = 0
correct_envelopes.each do |key, value|
  percent = ((value/simulations.to_f)*100)
  puts key.to_s + " correct: " + percent.to_s + "%"
  at_least_one_correct += percent if key > 0
end

# Print the "At least 1" result.
puts "At least 1 correct: " + at_least_one_correct.to_s + "%"