Answer: 34
If at least two students' scores must be the same, and there are only 5 possible scores (1, 2, 3, 4, or 5), then the maximum number of students who can have the same score is 36 - 2 = 34. This ensures that at least two students will have the same score, while still allowing for all 36 students to have a score from 1 to 5.