- 5th Jun 2019
- 04:45 am

**Question**

A school has 100 lockers and 100 students. All lockers are closed on the first day of school. As the students enter, the first student, denoted S1, opens every locker. Then the second student, S2, begins with the second locker, denoted L2, and closes every other locker. Student S3 begins with the third locker and changes every third locker (closes it if it was open, and opens it if it was closed). Student S4 begins with locker L4 and changes every fourth locker. Student S5 starts with L5 and changes every fifth locker, and so on, until student S100 changes L100. After all the students have passed through the building and changed the lockers, which lockers are open?

Write a program to find your answer.

**Answer**

public class Problem3 { public static void main(String[] args) { // TODO Auto-generated method stub // declare locker boolean[] locker; // allocates locker locker = new boolean[100]; // Init the locker for (int i = 0; i < 100; ++i) { locker[i] = false; } // logic int counter = 1; for (int i = 0; i < 100; ++i) { // the first student - Open very locker if (i == 0) { for (int j = i; j < 100; ++j) { locker[j] = true; } counter++; continue; } // the second student - Begin with the locker 2 and close every other locker if (i == 1) { for (int j = i; j < 100; ++j) { locker[j] = false; } counter++; continue; } // Logic for normal //System.out.print((i + 1) + " : "); for (int j = i; j < 100; ++j) { if (j % counter == i) { //System.out.print((j + 1) + " "); if (locker[j] == true) { locker[j] = false; } else { locker[j] = true; } } } //System.out.println(""); counter++; } for (int i = 0; i < 100; ++i) { if (locker[i] == true) { System.out.println("Locker " + (i + 1) + " is open"); } } } }