Weekly Puzzle#3: Problem solving

Write a program, solving problem below in any new for you language:

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
List lockers = 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.

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