I applied for a job in a small company (~25 employees) on December and after a month the CEO of the company wrote to me that he is interested to interview me. During the interview I got a bad impression of the employer and decided that I would not want to work for the company. However, the interviewer asked me whether I want to do a mini-project for them involving a complex but very interesting scientific problem. I told them I didn't mind, because I am interested anyway in this kind of work.
It took me 3days to a week to finish it. My technique would easily become much faster with a few more modifications, but I was not ready to invest more time and end up having my code stolen or used and getting the job denied. I am going to write a short description of the technicalities from which someone who is smart enough can see the extension to the technique I used to make it much faster.
I was thinking of licensing my code under MIT License and the documentations under something like creative commons. This will theoretically/psychologically gaurantee me that they won't steal the code (though they can steal it if they want and I wouldn't know). I am explaining in my documentation how the code could thereotically be improved in specific places and this will give them a gist of my abilities.
My question to the forum is: Am I being rude or "illegal" by trying to license the code and my text?
The problem was given to me as a pdf file and on the file it was written "for internal use only", I didn't sign any contract or made any promises. I feel this is the best way I can protect myself and I still want to solve the problem because of my interest in it and because this is the kind of work I want. Worst case is that I don't get the job but after this work I can almost publish a paper on this problem and at least improve my scientific profile.
Edit : Just to let you guys know. I decided to license my work and send it to them. For future applicants who have my situations, I will give an update of what happened.