If you don't have a Twitter account, you can take place in the contest by following Android in your circles on Google+. We would imagine that this could be like the contest that Radio Shack did for the HTC EVO 4G using their Twitter account back in September. Radio Shack's contest took place in one day with one phone won each hour for 9 hours. Expect questions about just about anything from math to physics to sports trivia, etc.
As an interesting side note, the 10th and last day of the contest is November 21st which has been rumored-along with November 17th-as being the expected launch date for the Samsung GALAXY Nexus on Verizon.
source: TheAndroidSite via AndroidCentral