Writing FizzBuzz without modulus division

fizzbuzz.rb

fizz    = [nil, nil, "Fizz"].cycle.take(100)
buzz    = [nil, nil, nil, nil, "Buzz"].cycle.take(100)
numbers = 1..100

numbers.zip(fizz, buzz) do |n, f, b|
  fizzbuzz = [f, b].join
  puts(fizzbuzz.empty? ? n : fizzbuzz)
end