Apple has launched its new “Countdown to 10 Billion Songs” promotion in celebration of the lead-up to the 10 billionth song sold on iTunes. In the contest, Apple is offering a $10,000 iTunes Gift Card to the person who downloads the 10 billionth song. No incremental prizes are being awarded, and there is a limit of 25 entries per person per day. As it has in past “countdown” promotions, the company is using a counter graphic on both its countdown webpage and iTunes store graphics, although these have normally been approximations, and not real-time download numbers. The contest begins today and will end once the 10 billionth download is reached; official rules are available here.