> You are mostly right, but are there any cases that a programmer wants to join a company and he can't even write a FizzBuzz program?

Maybe I'm just being cynical but once you get involved in the process of screening candidates you realize that people will literally apply to any job regardless of their ability to perform it. So yes, there are thousands of cases every day where someone wants a programming job and can't even write FizzBuzz.

> but are there any cases that a programmer wants to join a company and he can't even write a FizzBuzz program?

It's not even restricted to pogramming.

I've been involved in some recruitment for an English NHS trust, and people just apply whether they're qualified or not.

Some jobs have a hard requirement for a particular professional registration (you have to be a registered nurse, for example), and that will be clearly stated in the ads and job spec, but you still get people applying who are not nurses, and who don't even have any registration (allied health professionals).

You'll see someone who's done the equivalent of band 4 admin work, with maybe a bit of managements, applying for director level positions.

Yes. I've interviewed "developers" who failed FizzBuzz, and one who took 20 minutes to come up with a solution. I've never even specified a required language for it, and generally accepted pseudo-code.

> I have asked that question to all the programmers that I've worked with (with various levels of skill) and all of them can write it.

Then you now understand the standard of person that gets filtered out by fizzbuzz.

It happens. Interviewed somebody for my company and asked them to write a little bit of code that would print a Fibonacci sequence, one of the other old chestnuts. It didn't go well, and neither did his employment when my boss hired him anyway...