1
(define (special-digit x)
  (define (sumOfDigits num sum)
  (if (= num 0)
      sum
     (sumOfDigits (quotient num 10) (+ sum (modulo num 10)))))
  (if (= (quotient x 10) 0)
     x
     (special-digit (sumOfDigits x 0))))
3
(define (filtered-sum p? f)
  (define (helper xs index s)
    (if (empty? xs)
        s
        (if (p? (* index index))
            (helper (cdr xs) (+ index 1) (+ s (car xs)))
            (helper (cdr xs) (+ index 1) s))))
  (λ (xs) (f (helper xs 0 0))))
2
(define (find-max f a b)

  (define (changeByA scaleA scaleFuncResult max)
    (if (< scaleA a)
        max
        (if (> (f scaleA scaleFuncResult) max)
            (changeByA (- scaleA 1) (f scaleA scaleFuncResult) (f scaleA scaleFuncResult))
            (changeByA (- scaleA 1) (f scaleA scaleFuncResult) max))))

  (define (changeByB scaleB max)
    (if (= scaleB a)
        max
        (if (< max (changeByA (- scaleB 2) (f (- scaleB 1) scaleB) max))
               (changeByB (- scaleB 1) (changeByA (- scaleB 2) (f (- scaleB 1) scaleB) max))
               (changeByB (- scaleB 1) max))))
  (changeByB b (f (- b 1) b)))