My method and estimate:

• Google "guess half the average number". The first result is Guess 2/3 of the average on Wikipedia.
• Find that "When performed among ordinary people it is usually found that the winner guess is much higher than 0, e.g., 21.6 was the winning value in a large internet-based competition organized by the Danish newspaper Politiken."
• Assume that these participants will follow the same algorithm, and note that 21.6 is slightly under what we'd get if nearly everyone thought "the average of all numbers is 50, so 2/3 that is 33, which will be the average, so I'll pick 2/3 of that which is 22".
• Pick something slightly under 50% * 50% * 50 = 12.5. Like 11.

The actual answer was 11.53.

(Full disclosure: actually first I picked 24 = something slightly under 50%*50, because I don't even know why, then later my brain said "hey why'd you do that??" and I picked 11 under a new name Guy "Oops" Srinivasan.)