In the new TV game-show "Zero to a Million", each player chooses a number in the range from 0 to 1,000,000. The mean of all the numbers is calculated and the mean is multiplied by 2/3. The person who chose the number closest to the result wins.
1. In order to maximize your odds of winning, which number would you choose?
2. If only integers were allowed, how would this affect your choice?
3. What would you choose if the prize equaled the winner's number in dollars?