Generate three different random numbers

You can use random.sample to get any amount of unique 'random' items from an iterable- there is no need to use nested loops:

>>> option1, option2, option3 = random.sample(range(1, 4), 3)
>>> option1, option2, option3
(3, 1, 2)

The bug in your code is that if option1 and option2 are different, the first while won't be entered, and you won't examine if any of them are equal to option3.