The Countdown Round is the most exciting round of the day. Based on the Sprint Round and Target Round scores, the top ten individuals are chosen to compete head-to-head. A math problem is projected on the screen, and two Mathletes race to finish it. There is a maximum of 45 seconds for each problem, but the main time limit is to finish the problem before one's opponent does. As soon as one student has found an answer, he or she buzzes in--this is super-fun when there are real buzzers!--and gives the answer orally. If, gosh forbid, that answer is wrong, then the other student has the rest of the 45 seconds to buzz in and answer.
Calculators are NOT allowed. A more detailed explanation of the Countdown Round rules can be found on the official Mathcounts website.
If you've made it to the Countdown Round, I first of all congratulate you. I sincerely hope that you find it an exciting experience as opposed to a traumatic one. Now, for a few tips.
A lot of Mathletes find the Countdown Round nerve-wracking. With the fast pace and all the eyes looking at you, it can seem like a high-pressure situation. Well, in terms of the competition, it really isn't. Even if the Countdown Round in your area affects your overall ranking, you can't fall from, say, 2nd place to 7th place. The way that the tournament is designed, your rank can go up by a lot, but it can go down only one place lower. You could move from 10th place to 1st place (and I've seen it done). But if you're already in 1st place, you could drop no lower than 2nd place. Basically, calm down! You have little to lose!
Unless you are on the borderline of qualifying for the team for the next level, in which case...I'll be honest, you do have a lot to lose. Go ahead and be nerve-wracked. (I'm just kidding, of course. Take deep breaths and try to relax, no matter what!)
When the problem shows up on the screen, read it to yourself and start working immediately. An announcer will probably read the problem aloud, but do NOT wait for him/her to finish reading. It will slow you down too much. At times, Mathletes will buzz in before the announcer has even finished reading the problem.
If you hear your opponent buzz in before you, don't stop working. Keep working because there's a possibility that your opponent's answer is incorrect, in which case you'll still have an opportunity to answer. Do, however, listen to your opponent's answer so that you don't give the same incorrect answer. (That would not only be incorrect but also embarrassing!)
If your opponent has already answered incorrectly, you have the rest of the 45 seconds to go. Take advantage of this. Slow down a little to be more careful. If there are still, say, 30 seconds left, there is no advantage in buzzing in immediately. Maybe you could check your answer quickly in your head. Theoretically, you could check and re-check your answer all the way until the 44th second!
But before your opponent and you have buzzed in... Now, that's a horse of a different color. Work at breakneck speed. Do NOT check your answer beyond a simple glance. Buzz in right away. Follow your instinct. Once, during a State Countdown Round, I glanced at the problem and saw something about areas of squares and the number 4. Immediately, the number 2 popped into mind because it was the square root of 4. Trusting my gut, I buzzed in and said "Two," as confidently as I could muster. I was right. It was beautiful.