billc

9/2/2014 - 6:18 PM

1000 Lockers Math Problem - Solved in Dart

```
/*
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?
*/
import 'dart:io';
int numberOfLockers = 1000;
// Lockers start all open because of the first student
List<String> lockers = new List.filled(numberOfLockers + 1, 'open');
main() {
for (var student = 2; student <= numberOfLockers; student++) {
// For the student, open the locker if closed, or close if open
for (var locker = student; locker <= numberOfLockers; locker += student) {
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 <= numberOfLockers; 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.
```