I am a junior in high school, and our school requires us to do a research project on some topic of our choice. I wanted to research on some combinatorial game, and I came up with Liar Games. I read a little bit about the type of questions that one can ask (Arbitrary yes-no, Prefix Questions, Variable Cost), and was wondering if the following was worth research/is not trivial:
It would just be a standard Remyi Ulam Liar Game, but there would be a variation in the type of question asked. Instead of asking a regular prefix question (asking whether the binary representation of the number begins with a particular sequence), I was thinking about asking whether the binary representation of the number has a particular substring in it.
For example: If I were guessing a number between 1 and 200 I could ask if the binary form had 1011 as a substring, instead of asking if the number started out with 1011. Most papers I read about prefix questions always reduced the question to searching for a particular vertex within a tree. Doing this variation could be open to a different approach.
I suppose asking whether the binary form had a particular subsequence would make the problem more computationally difficult, and make it easier for me to contribute something novel.
In short, does anyone know if attempting something like this is not worthwhile (eg. It's already been done, It's trivial, etc.)
Thank you!