"I could feel my frustration rise as I am struggling to come up with a solution on a whiteboard....yep, I am definitely not going to pass this interview. I ran out of time before coming up with a working solution."
Instead of standing there with nothing its better to be straight up and just say "No idea mate" and then name reasons why that is but how you'd solve it in a normal situation. It is a lot about human psychology, showing them that they want/need you, not vice versa.
Sometimes all it takes is balls and a good amount of "I don't give a fuck" attitude.
I wouldn't let anyone treat me like Sahat got treated.