; compute the sum of a list of numbers lon
; examples:
; (sum '(2 4 8 2)) -> 16
; (sum '()) -> 0

(define (sum lon)
  (if (null? lon) 
      0
      (+ (car lon) (sum (cdr lon)))))

; compute the sum of squares for a list of numbers lon
; examples
; (sum-of-squares '()) -> 0
; (sum-of-squares '(3 4)) -> 25
; (sum-of-squares '(2 2 2 2)) -> 16

(define (sum-of-squares lon)
  (if (null? lon)
      0
      (+ (* (car lon) (car lon)) (sum-of-squares (cdr lon)))))

; compute the length of a diagonal for an nd box with
;  dimensions given by list of numbers
;  dimensions-of-box
; examples
; (length-of-diagonal '(3 4)) -> 5
; (length-of-diagonal '(2 2 2 2)) -> 4

(define (length-of-diagonal dimensions-of-box)
  (sqrt (sum-of-squares dimensions-of-box)))

; switch is either 'on or 'off
; (flip switch) is what you get when you flip 
; examples
; (flip 'on) -> 'off
; (flip 'off) -> 'on

(define (flip switch)
  (if (eq? 'off switch) 
      'on
      'off))

; determine the state of a light bulb controlled
; by n hotel switches linked together, assuming
; the switches are in the states specified by
; list los
; computes nary xor (parity)
; examples
; (light-bulb-state '(on)) -> 'on
; (light-bulb-state '(off on)) -> 'on
; (light-bulb-state '(on on)) -> 'off
; (light-bulb-state '(off on off on on)) -> 'on

(define (light-bulb-state los)
  (if (null? los)
      'off
      (let ((state (light-bulb-state (cdr los))))
        (if (eq? 'on (car los))
            (flip state)
            state))))