I am a high school sophomore who is interested in computer science. I developed a cool algorithm for #SAT, and I'm implementing and doing a science fair project on it. My adviser, who is the best science teacher at my school and is also the AP Comp Sci teacher, told me that she has absolutely no idea what my project is about, and that I need to be able to briefly explain her why #SAT is important in under 5 minutes. I told her SAT reduces to #SAT and tried to explain why SAT is important: I gave her some examples of NP problems, explained her how problems in NP reduce to SAT, and explained how with binary search you can reduce certain optimization problems to SAT, which allows you to fold proteins and make powerful AI models. Unfortunately, she didn't understand me at all. Could you give me a few pointers?P.S. My adviser asked me what useful problems reduce to #SAT that don't reduce to SAT (assuming some problems in #P are harder than their corresponding NP versions). All I could come up with was finding how many models for a given data set are better than a given model (assuming each parameter of the model is smaller than a given number of bits). I looked for other ones on the web but I couldn't find anything I could understand. Are there any other good applications?
Explaining SAT to high school science teachers
algorithms;satisfiability