/// Problem statement: There are n doors and n students.
/// Initially all doors are closed.
/// Then each student goes and perform the following
/// kth student toggle door number k, 2k, 3k .... etc
/// For ex: Student 1 toggles all door (If it is open, close it and vice-versa)
///         Student 2 toggles door number 2, 4, 6, .... 96, 98, 100
///         ...
/// Find the number of open doors if the number of students is 100
#include <iostream>
#include <algorithm>
using namespace std;

int main() {
  const int numDoors = 100;
  bool doors[numDoors];
  for(int i = 1; i <= numDoors; ++i) doors[i-1] = i > numDoors / 2;
  for(int i = 1; i <=  numDoors / 2; ++i) {
    for(int j = i; j <= numDoors; j += i) {
      doors[j-1] ^= true;
    }
  }
  cout << "Number of open doors = " << count( doors, doors + numDoors, true ) << endl;
}

Number of open doors = 10