If I couldn't solve a problem on my technical interview, does it mean I most likely automatically didn't pass the round?

I won’t say that technical problems presented in an interview are designed not to be solved, but their evaluative usefulness is clearly diminished if the answer is too easily derived by too many candidates, or they fail to showcase enough of the capabilities I mentioned above.

Not necessarily. Interviewers are usually more interested in seeing the approach you take to solving the problem, how you respond to guidance from the interviewer, and whether you can respond effectively to new information or changes in assumptions that the interviewer might give you.

I won’t say that technical problems presented in an interview are designed not to be solved, but their evaluative usefulness is clearly diminished if the answer is too easily derived by too many candidates, or they fail to showcase enough of the capabilities I mentioned above.

In my day-to-day role, I see more or less all of the interview feedback submitted on candidates being considered for internship and other positions. Many, many candidates advance to later interview rounds without getting a completely ‘right’ answer to every question.