<p>There's a math contest called the USAMTS, stands for the USA Mathematical Talent Search. You have ONE MONTH to complete each round, which consists of 5 problems. You can use computers, books, etc. Some of the problems are pretty hard, some are pretty easy. At the end of the year, you can get Gold, Silver, Bronze, Honorable Mention, depending on your score range. It's not too difficult either; a score of 40/100 will earn you honorable mention. see usamts.org for more info! sponsered by AOPS and Google.</p>
<p>Yeah I tried it this year (in the middle of the season) and I thought it was pretty rewarding. You get feedback to all your solutions. And did I mention the program is free?</p>