simulation of the math problem: "If you break a straight line randomly in two places, what is the probability that you can form a triangle from the resulting three pieces?"

triangles-sim.rb

# simulation to calculate an answer to the question:
#
# "If you break a straight line randomly in two places, what is the probability that you can
# form a triangle from the resulting three pieces?"
#
# usage: ruby ./triangles-sim.rb [trials]
# sample output:
#
# $> ruby ./triangles-sim.rb 1000000
#
# Trials: 1000000
# Valid Triangles: 250077
# Percentage: 25.0077%
#
# Ran in 2.775591s

started = Time.new

trials        = ARGV.length > 0 ? ARGV[0].to_i : 1000
triangleCount = 0

# let's assume the starting length is 1 so we can use rand
trials.times do
  breaks = [rand, rand].sort

  # calc the lengths
  lengths = [breaks[0], breaks[1] - breaks[0], 1 - breaks[1]].sort

  # add 1 if we have a valid triangle (sum of two smaller lengths must be less
  # than largest length)
  triangleCount += 1 if lengths[2] < lengths[0] + lengths[1]
end

pct = triangleCount.to_f / trials * 100

runtime = Time.new - started

puts
puts "Trials: #{trials}"
puts "Valid Triangles: #{triangleCount}"
puts "Percentage: #{pct}%"
puts
puts "Ran in #{runtime}s"