Ask HN: Can I openly publish a project given to me at a job interview?

I had a job interview in which the interviewer assigned me a small project (provided test data, project objective, and performance measure) as part of the interview process to evaluate my capability. I ended up not working for that company, but I would like to publish the code I wrote for that small project. I did not get paid or sign anything with that company.

The data the company provided can be downloaded online. So I can use any other data for testing my code.

Would there be any trouble if I publish the small project (as a scientific paper, or an open source code)?