1000 lockers problem

; 1000 lockers problem
; as in http://www.reddit.com/r/dailyprogrammer/comments/ruiob/452012_challenge_36_easy/
(define this-many-lockers 1000)
(define locked #t)
(define lockers (make-vector this-many-lockers locked))

(define (toggle! locker)
  (let ((n (+ -1 locker))) ; because vectors are zero-based but lockers begin from 1
    (vector-set! lockers n (not (vector-ref lockers n)))))

(define (open? locker) (not (vector-ref lockers (+ -1 locker))))

(define (multiples n upto)
  (let f ((x 1))
    (let ((m (* x n)))
      (if (> m upto) `()
          (cons m (f (+ 1 x)))))))

(let unleash ((student 1))
  (if (> student this-many-lockers) 'gone
      (begin
        (for-each (lambda (x) (toggle! x)) (multiples student this-many-lockers))
        (unleash (+ 1 student)))))

(define open-lockers
  (let check ((l 1))
    (if (> l this-many-lockers) `()
        (if (open? l)
            (cons l (check (+ 1 l)))
            (check (+ 1 l))))))

(length open-lockers)
open-lockers