4. (25 p.) In a class consisting of 100 students, the professor makes the following an nouncement: \"all of you must simultaneously and independently write a number be tween 0 and 100 on a piece of paper, and give it to me. I will calculate the average of all the submitted numbers. Lets call this average 33. The target number will be :I: 40 +2 The student whose submitted number is closest to the target wins $100. If there is a tie for rst place, those who came closest will share the $100 (for example, if four stu dents tie for rst, each gets $25)\". What is the (pure strategy) Nash equilibrium? We want to know the exact numerical value each student submits. Emplam your reasoning