Recursively adding the digits of a multiple of 3 until there is only one digit left and it is one of 3, 6 or 9 shows that it is a multiple of 3 as shown in this script that compares it to the modulo method

gistfile1.rb

#!/usr/bin/ruby
i=0
while(i<300)
  puts "mod: #{i}" if i % 3 == 0
  string = i.to_s
  while string.length > 1
    total = 0
    string.split('').each {|x| total += x.to_i}
    string = total.to_s
  end
  puts "add: #{i}" if [3,6,9].include? total
  i+=1
end