Question

I need help writing a program for this assignment

Problem: Locker puzzle A school has 100 lockers and 100 students. All lockers are locked on the first day of school. As the students enter, the 1st student opens every locker. Then the 2nd student, begins with the 2nd locker, closes every other locker. The 3rd student begins with the 3rd locker and changes every 3rd locker (closes it if it's open and opens it if its closed). The 4th student begins with the 4th locker and changes every 4th locker. The 5th students begins with 5h locker and changes every 5th locker, and so on, until the 100th student changes the 100th locker.

Answer 1

This is easy. Lets define the state of the locker as open or closed. At any given point in time we know that a locker will be in one of these two states. Lets say we denote open state by 1 and closed state by 0. so we have to print all the lockers with open state which is 1 at the end of the task. We can do this in the following way.

Code :

#include <iostream>

using namespace std;

int main() {

//set all lockers state to closed

int lockers[101]={0};

for(int i = 1;i<=100;i++){

//we will start from ith locker for ith student

for(int j=i;j<=100;j=j+i){

//toggle the state of the lockers

lockers[j]=1-lockers[j];

}

}

for(int i =1;i<=100;i++){

if(lockers[i]==1){

cout<<i<<" ";

}

}

cout<<endl;

return 0;

}

OUTPUT :

1 4 9 16 25 36 49 64 81 100