The article conceit is fantastic. That said, is the going-in algo wrong?

I see a case for 3 * 5 in here:

  for n in range(1, 101):
      if n % 15 == 0:
          print('FizzBuzz')
      elif n % 3 == 0:
          print('Fizz')
      elif n % 5 == 0:
          print('Buzz')
      else:
          print(n)

Why?

If we add 'Bazz' for mod 7, are we going to hardcode:

  for n in range(1, 105):
      if n % 105 == 0:          # 3 * 5 * 7
          print('FizzBuzzBazz')
      elif n % 15 == 0:         # 3 * 5
          print('FizzBuzz')
      elif n % 21 == 0:         # 3 * 7
          print('FizzBazz')
      elif n % 35 == 0:         # 5 * 7
          print('BuzzBazz')
      elif n % 3 == 0:
          print('Fizz')
      elif n % 5 == 0:
          print('Buzz')
      elif n % 7 == 0:
          print('Bazz')
      else:
          print(n)

Or should we have done something like:

  for n in range(1, 105):
      out = ''
  
      if n % 3 == 0:
          out += 'Fizz'
      if n % 5 == 0:
          out += 'Buzz'
      if n % 7 == 0:
          out += 'Bazz'
  
      print(out or n)

I've been told sure, but that's a premature optimization, 3 factors wasn't in the spec. OK, but if we changed our minds on even one of the two factors, we're having to find and change 2 lines of code ... still seems off.

Sort of fun to muse whether almost all FizzBuzz implementations are a bit wrong.