I've done a fair amount of hiring at startups. The main thing I looked for was years of experience and previous job title. I never cared what the person wore, as long as it was appropriate. A cover letter was nice, but I didn't use it as a filter...I was more concerned with the information contained in the cover letter than whether or not it was there.
The biggest thing is to give people information about you. The math contest thing would stand out because it's unique and somewhat interesting, but it wouldn't be particularly important for any of the positions I hired for. I was far more impressed by previous job titles (ie, "Intern, Google Inc") than I was any of the extracurricular stuff.
If you don't have any previous experience, the most important things are an impressive GPA (3.8+) or some kind of impressive course work, such as an artificial intelligence project or ideally a startup of your own.
The biggest thing is to give people information about you. The math contest thing would stand out because it's unique and somewhat interesting, but it wouldn't be particularly important for any of the positions I hired for. I was far more impressed by previous job titles (ie, "Intern, Google Inc") than I was any of the extracurricular stuff.
If you don't have any previous experience, the most important things are an impressive GPA (3.8+) or some kind of impressive course work, such as an artificial intelligence project or ideally a startup of your own.