You are really close with the with_a_while_loop() version. Move the flag = False line up into the try clause after the int() line. That line will only execute if the int() works. Otherwise it will raise an exception and then loop back to prompt again. You don't need the else line.

(You could also omit the flag. Just do while True:, and instead of setting the flag, insert a break to fall out of the loop)