Exercise 1.14

(define (count-change amount) 
  (define (cc a n) 
  (cond ((< a 0) 0) 
        ((= a 0) 1) 
        ((= n 0) 0) 
        (else (+ (cc a (- n 1)) 
                 (cc (- a (first-denomination n)) n))))) 
  (cc amount 5)) 

(define (first-denomination kinds-of-coins) 
  (vector-ref '#(1 5 10 25 50) (- kinds-of-coins 1))) 

(count-change 100) => 292

(count-change 11) => 4

(cc 11 5)
  (cc -39 5) => 0
  (cc 11 4)
    (cc -14 4) => 0
    (cc 11 3)
      (cc 1 3)
        (cc -9 3) => 0
        (cc 1 2)
          (cc -4 2) => 0
          (cc 1 1)
            (cc 0 1) => 1
            (cc 1 0) => 0
      (cc 11 2)
        (cc 6 2)
          (cc 1 2)
            (cc -4 2) => 0
            (cc 1 1)
              (cc 0 1) => 1
              (cc 1 0) => 0
          (cc 6 1)
            (cc 5 1)
              (cc 4 1)
                (cc 3 1)
                  (cc 2 1)
                    (cc 1 1)
                      (cc 0 1) => 1
                      (cc 1 0) => 0
                    (cc 2 0) => 0
                  (cc 3 0) => 0
                (cc 4 0) => 0
              (cc 5 0) => 0
            (cc 6 0) => 0
        (cc 11 1)
          (cc 10 1)
            (cc 9 1)
              (cc 8 1)
                (cc 7 1)
                  (cc 6 1)
                    (cc 5 1)
                      (cc 4 1)
                        (cc 3 1)
                          (cc 2 1)
                            (cc 1 1)
                              (cc 0 1) => 1
                              (cc 1 0) => 0
                            (cc 2 0) => 0
                          (cc 3 0) => 0
                        (cc 4 0) => 0
                      (cc 5 0) => 0
                    (cc 6 0) => 0
                  (cc 7 0) => 0
                (cc 8 0) => 0
              (cc 9 0) => 0
            (cc 10 0) => 0
          (cc 11 0) => 0