When brevity doesn't matter...

when_brevity_is_not_a_thing.rb

# Run if necessary:
# RubyVM::InstructionSequence.compile_option = {
#   tailcall_optimization: true,
#   trace_instruction: false
# }

class FizzBuzz
  def self.find_answers_for(max)
    self.new(max).find_answers_for([], 1)
  end

  def initialize(max)
    @max = max
    @fizz = 1
    @buzz = 1
    @fizzbuzz = 1
  end

  def find_answers_for(acc, count)
    return acc if count > @max

    result = compute(count)
    advance_state

    find_answers_for(
      acc << result,
      count + 1
    )
  end

  private

  def advance_state
    advance_fizz
    advance_buzz
    advance_fizzbuzz
    nil
  end

  def advance_fizz
    @fizz = @fizz == 3 ? 1 : @fizz + 1
  end
  def advance_buzz
    @buzz = @buzz == 5 ? 1 : @buzz + 1
  end
  def advance_fizzbuzz
    @fizzbuzz = @fizzbuzz == 15 ? 1 : @fizzbuzz + 1
  end

  def compute(count)
    if @fizzbuzz == 15
      "fizzbuzz"
    elsif @buzz == 5
      "buzz"
    elsif @fizz == 3
      "fizz"
    else
      count.to_s
    end
  end
end

puts Benchmark.measure { FizzBuzz.find_answers_for(10000) }
#  0.400000   0.030000   0.430000 (  0.422816)