[cevaris]

> Maybe I should refer to myself as software designer rather than programmer.

I think you should refer to yourself as an Software developer, not a Software Engineer. You can be good by referencing your previous experiences. But knowing how to solve and loving puzzles is a nice sign that this individual can solve problems quick and efficiently. This latter case is less common though. Most programmers are Software Developers, just referencing sdk's and frameworks and minor "new" development.