game theory, 70% game

[flopdanutz]

My game theory class for econ has 150 students.

last week the professor offered $10 to the winner of the following game.
Each student chooses 1 integer between 1 and 100 (1 being the minimum; 100 being the maximum). The professor calculated the winning number by taking the average of the numbers and multiplying that number by the ratio 7/10 (70% or 0.7). The student that gave the response closest to that number wins, in case of ties a student would be randomly chosen from the groups that tied.

What number would you choose and why? guess what number was the winning number? Do you think people think rationally?

I actually expect the results on this board will be drastically different from my econ class due to my perception that people here utilize game theory and strategic dominance more. The reuslts of the class outcome will be given later (after a few of you post)