Ex-2.40,2.41

2.40

(define (unique-pairs n)
  (accumulate
   (lambda (x y) 
     (append (map (lambda (z)
            (cons x z)) (enumerate-interval 1 (- x 1))) y))
   nil (enumerate-interval 1 n)))

(define (prime-sum-pairs n)
  (filter prime-sum?
          (map
           (lambda (x)
             (list (car x) (cdr x) (+ (car x) (cdr x))))
           (unique-pairs n))))

2.41

;this generates ordered triples of distinct positive
;integers i, j, and k less than or equal to a given
;integer n

(define (enumerate-all-triplets n)
  (flatmap (lambda (x) x)
   (map
    (lambda (x)
      (map (lambda (y)
             (list y (car x) (cdr x)))
           (enumerate-interval (+ (car x) 1) n)))
    (unique-pairs n))))

(define (triplet-with-sum-s n s)
  (filter (lambda (x)
            (= s
               (+ (car x) (cadr x) (caddr x))))
          (enumerate-all-triplets n)))