Java Program Scenario: A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, the principal plays the following game: She asks the first student to open all the lockers. She then asks the second student to close all the even-numbered lockers. The third student is asked to check every third locker. If it is open, the student closes it; if it is closed, the student opens it. The fourth student is asked to check every fourth locker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continue this game. In general, the nth student checks every nth locker. If the locker is open, the student closes it; if it is closed, the student opens it. After all the students have taken their turns, some of the lockers are open and some are closed. Write a program that prompts the user to enter the number of lockers in a school. After the game is over, the program outputs the number of lockers and the locker numbers of the lockers that are open. Test run your program for the following inputs: 1000, 5000, 10000. Do you see any pattern developing for the locker numbers that are open in the output? (Hint: Consider locker number 100. This locker is visited by student numbers 1, 2, 3, 5, 6, 10, 15, and 30. Note that if the number of positive divisors of a locker number is odd, then at the end of the game the locker is open. If the number of positive divisors of a locker number is even, then at the end of the game the locker is closed.)
Java Program
Scenario:
A high school has 1000 students and 1000 lockers, one locker for each student. On the
first day of school, the principal plays the following game: She asks the first student to open all the lockers. She then asks the second student to close all the even-numbered lockers. The third student is asked to check every third locker. If it is open, the student closes it; if it is closed, the student opens it. The fourth student is asked to check every fourth locker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continue this game. In general, the nth student checks every nth locker. If the locker is open, the student closes it; if it is closed, the student opens it. After all the students have taken their turns, some of the lockers are open and some are closed. Write a program that prompts the user to enter the number of lockers in a school. After the game is over, the program outputs the number of lockers and the locker numbers of the lockers that are open. Test run your program for the following inputs: 1000, 5000, 10000. Do you see any pattern developing for the locker numbers that are open in the output?
(Hint: Consider locker number 100. This locker is visited by student numbers 1, 2, 3, 5, 6, 10, 15, and 30. Note that if the number of positive divisors of a locker number is odd, then at the end of the game the locker is open. If the number of positive divisors of a locker number is even, then at the end of the game the locker is closed.)
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