; the 147 puzzle

(define (f k)
  (let ((fss (list)))
    (let loop1 ((k k) (n 1) (d 1) (fs (list)))
      (if (= k 1)
          (if (zero? (modulo d n))
            (set! fss (cons (cons (/ d n) fs) fss)))
          (let ((lo (if (null? fs) (+ (quotient d n) 1)
                      (max (car fs) (+ (quotient d n) 1))))
                (hi (quotient (* k d) n)))
            (let loop2 ((a lo))
              (when (<= a hi)
                (let* ((new-d (lcm a d))
                       (new-n (- (* n new-d (/ d)) (/ new-d a))))
                  (loop1 (- k 1) new-n new-d (cons a fs)))
                (loop2 (+ a 1)))))))
    (reverse (map reverse fss))))

(for-each
  (lambda (x) (display x) (newline))
  (f 5))

(2 3 7 43 1806)
(2 3 7 44 924)
(2 3 7 45 630)
(2 3 7 46 483)
(2 3 7 48 336)
(2 3 7 49 294)
(2 3 7 51 238)
(2 3 7 54 189)
(2 3 7 56 168)
(2 3 7 60 140)
(2 3 7 63 126)
(2 3 7 70 105)
(2 3 7 78 91)
(2 3 7 84 84)
(2 3 8 25 600)
(2 3 8 26 312)
(2 3 8 27 216)
(2 3 8 28 168)
(2 3 8 30 120)
(2 3 8 32 96)
(2 3 8 33 88)
(2 3 8 36 72)
(2 3 8 40 60)
(2 3 8 42 56)
(2 3 8 48 48)
(2 3 9 19 342)
(2 3 9 20 180)
(2 3 9 21 126)
(2 3 9 22 99)
(2 3 9 24 72)
(2 3 9 27 54)
(2 3 9 30 45)
(2 3 9 36 36)
(2 3 10 16 240)
(2 3 10 18 90)
(2 3 10 20 60)
(2 3 10 24 40)
(2 3 10 30 30)
(2 3 11 14 231)
(2 3 11 15 110)
(2 3 11 22 33)
(2 3 12 13 156)
(2 3 12 14 84)
(2 3 12 15 60)
(2 3 12 16 48)
(2 3 12 18 36)
(2 3 12 20 30)
(2 3 12 21 28)
(2 3 12 24 24)
(2 3 13 13 78)
(2 3 14 14 42)
(2 3 14 15 35)
(2 3 14 21 21)
(2 3 15 15 30)
(2 3 15 20 20)
(2 3 16 16 24)
(2 3 18 18 18)
(2 4 5 21 420)
(2 4 5 22 220)
(2 4 5 24 120)
(2 4 5 25 100)
(2 4 5 28 70)
(2 4 5 30 60)
(2 4 5 36 45)
(2 4 5 40 40)
(2 4 6 13 156)
(2 4 6 14 84)
(2 4 6 15 60)
(2 4 6 16 48)
(2 4 6 18 36)
(2 4 6 20 30)
(2 4 6 21 28)
(2 4 6 24 24)
(2 4 7 10 140)
(2 4 7 12 42)
(2 4 7 14 28)
(2 4 8 9 72)
(2 4 8 10 40)
(2 4 8 12 24)
(2 4 8 16 16)
(2 4 9 9 36)
(2 4 9 12 18)
(2 4 10 10 20)
(2 4 10 12 15)
(2 4 12 12 12)
(2 5 5 11 110)
(2 5 5 12 60)
(2 5 5 14 35)
(2 5 5 15 30)
(2 5 5 20 20)
(2 5 6 8 120)
(2 5 6 9 45)
(2 5 6 10 30)
(2 5 6 12 20)
(2 5 6 15 15)
(2 5 7 7 70)
(2 5 8 8 20)
(2 5 10 10 10)
(2 6 6 7 42)
(2 6 6 8 24)
(2 6 6 9 18)
(2 6 6 10 15)
(2 6 6 12 12)
(2 6 7 7 21)
(2 6 8 8 12)
(2 6 9 9 9)
(2 7 7 7 14)
(2 8 8 8 8)
(3 3 4 13 156)
(3 3 4 14 84)
(3 3 4 15 60)
(3 3 4 16 48)
(3 3 4 18 36)
(3 3 4 20 30)
(3 3 4 21 28)
(3 3 4 24 24)
(3 3 5 8 120)
(3 3 5 9 45)
(3 3 5 10 30)
(3 3 5 12 20)
(3 3 5 15 15)
(3 3 6 7 42)
(3 3 6 8 24)
(3 3 6 9 18)
(3 3 6 10 15)
(3 3 6 12 12)
(3 3 7 7 21)
(3 3 8 8 12)
(3 3 9 9 9)
(3 4 4 7 42)
(3 4 4 8 24)
(3 4 4 9 18)
(3 4 4 10 15)
(3 4 4 12 12)
(3 4 5 5 60)
(3 4 5 6 20)
(3 4 6 6 12)
(3 4 6 8 8)
(3 5 5 5 15)
(3 5 5 6 10)
(3 6 6 6 6)
(4 4 4 5 20)
(4 4 4 6 12)
(4 4 4 8 8)
(4 4 5 5 10)
(4 4 6 6 6)
(5 5 5 5 5)