As an employer, I would not want you to do this. If I wanted the questions posted on a website, I'd do it myself and refer everyone to it. I also wouldn't post answers from each candidate online, nor would I want candidates to post their own answers online. Being able to read answers from other candidates before providing your own answer would create an unfair advantage. It wouldn't demonstrate whether or not you knew the answer to begin with, and it would limit your ability to show unique insight into the problem or solution.
I am all for you creating a portfolio that demonstrates your skills and abilities. If the work in your portfolio was inspired by my interview questions, that's great, but please generalize so we can both achieve what we are trying to accomplish. Also, since your solution didn't get you the job, you might want to collect feedback from others and update it before posting it; otherwise you could just as easily be demonstrating why not to hire you.