A national math contest consisted of 11 multiple choice questions, each having 11 possible answers. Suppose that 111 students actually wrote the exam, and no two students has more than one answer in common. The highest possible average mark for the students can be expressed as a/b where a,b are coprime positive integers. What is the value of a+b?

To find the highest possible average mark for the students, we need to maximize the total number of correct answers among all the students.

Since each question has 11 possible answers, the maximum number of students who can have the same correct answer for a particular question is 11. Therefore, in order to maximize the total number of correct answers, we should assign different correct answers to different questions for each student.

Let's assume the first student has question 1 as correct, the second student has question 2 as correct, and so on until the eleventh student who has question 11 as correct.

Now, for the twelfth student, we cannot assign any of the previously assigned questions as correct because it would violate the condition that no two students have more than one answer in common. Therefore, the twelfth student must have a new and different question as correct.

Following the same logic, each subsequent student must have a new and different question as correct.

Thus, the total number of correct answers among all the students would be 11 + 10 + 9 + ... + 2 + 1 = 66.

Since there are 111 students, the average mark for each student would be 66/111 = 2/3.

Therefore, the value of a + b is 2 + 3 = 5.