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After the first student, all of the lockers are open.
After the second student, all of the lockers with even numbers will be closed. This means that lockers 2, 4, 6, 8, etc. will be closed and lockers 1, 3, 5, 7, etc. will remain open.
After the third student, the lockers with numbers that are multiples of 3 will be changed. This means that lockers 3, 6, 9, 12, etc. will be closed (since they were originally open) and lockers 1, 2, 4, 5, 7, 8, 10, 11, etc. will remain open.
Therefore, after the first three students, locker 6 will be closed.