I'm going to be a junior next year, and our school requires us to make a science fair project. I've always been interested in math and am heavily involved in math contests. However, for the past few years, all my projects have been coding related. This year, however, I really want to do a math research project.
In particular, I was reading some papers about Ulam's liar game and was really interested in it. However, I couldn't think of any new research that could come from the topic. I know certain kinds of error correcting codes have a relationship with the game, but I'm just not sure how to proceed.
Could anyone point me towards some other papers or ideas, or perhaps help me formulate an idea. To give you an idea of my mathematical background, I usually get around 7- 10s on AIMEs (if you know what that is) and I enjoy proving things (particularly combinatorics). My background in linear algebra is limited at best, although I can definitely learn it.