Apex Doors

List<boolean> lockers = new List<boolean>();
for(integer s = 0; s< 1000; s++){
    for (integer i = s; i < 1000; i += (s+1)){
        if(s == 0) {
            // First Student Opens every locker
    		lockers.add(true);
        } else {
            // nth student toggles every nth locker
        	lockers[i] = !lockers[i];
        }
    }    
}

for (integer i = 0; i < 100; i++) {
    System.debug((i+1) + ': ' + (lockers[i]?'🚪 (open)':'_ (Closed)'));
}

Brute force maths for https://twitter.com/FishOfPrey/status/991860727769018368