# Weekly Puzzle#3: Problem solving

There are 1000 lockers in a high school with 1000 students. The

problem begins with the first student opening all 1000 lockers; next

the second student closes lockers 2,4,6,8,10 and so on to locker 1000;

the third student changes the state (opens lockers closed, closes

lockers open) on lockers 3,6,9,12,15 and so on; the fourth student

changes the state of lockers 4,8,12,16 and so on. This goes on until

every student has had a turn.

How many lockers will be open at the end? What is the formula?

Find solution in Dart below:

import 'dart:io';

int numberOfLockers = 1000;

// Lockers start all open because of the first student

Listlockers = new List.filled(numberOfLockers + 1, 'open'); main() {

for (var student = 2; student

// For the student, open the locker if closed, or close if open

for (var locker = student; locker lockers[locker] = lockers[locker] == 'open' ? 'closed' : 'open';

}}

// Count of lockers remaining open

int total = 0;// List the lockers that remain open

for (var locker = 1; locker if (lockers[locker] == 'open') {

stdout.write("${locker} ");

total += 1;

}

}print("\nThere are ${total} lockers remaining open.");

}// 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 841 900 961

// There are 31 lockers remaining open.