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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.

Thanks!

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    $\begingroup$ Are you supposed/allowed to have an advisor? Even university graduate research is usually done with the help of an experienced scientist, I think high school research should have one as well. Not that I discourage you to proceed on your own, especially if you have experience already. $\endgroup$ – Yuriy S May 2 at 17:40
  • $\begingroup$ What niveau is expected of the project? All I know about science fairs (from US TV shows) is that there is always a baking sode vulcano ... $\endgroup$ – Hagen von Eitzen May 2 at 17:43
  • $\begingroup$ @YuriyS, there is an advisor for the entire class. However, her expertise is in chemistry and she prefers to stay out of projects that she can't help much in. However, there is nothing wrong with asking a university professor for help. $\endgroup$ – FrasierCrane May 2 at 17:46
  • $\begingroup$ @HagenvonEitzen The level is actually surprisingly high. Here are some other mathematics projects submitted: abstracts.societyforscience.org However those were only the best of their regional science fair. However, I would prefer my project to be of somewhat high quality. $\endgroup$ – FrasierCrane May 2 at 17:48
  • $\begingroup$ If you want to choose the topic yourself, and you like coding, I would suggest something related to cellular automata. It's a popular and rich area, and surprisingly simple to investigate experimentally $\endgroup$ – Yuriy S May 2 at 18:12

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