Question

Lockers numbered 1 to 100 stand in a row. A student stops by and opens all the lockers. Asecond student then comes by and closes all the even numbered lockers. A third student thencomes along and changes the state of all the lockers which are multiples of 3. This processcontinues until all 100 students have been through. Which lockers are now open?

Answer 1

34 lockers are open

Explanation:

locker numbers 1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 39, 41, 43, 47, 49, 53, 55, 59, 61, 65, 67, 71, 73, 77, 79, 83, 85, 89, 91, 95, and 97 are open