Project Euler

[ホーム](https://redmine.noppi.jp) - [[Wiki|Project Euler]]

# [[Problem 56]]

## Powerful Digit Sum

A googol ($10^{100}$) is a massive number: one followed by one-hundred zeros; $100^{100}$ is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is only $1$.

Considering natural numbers of the form, $a^b$, where $a, b \lt 100$, what is the maximum digital sum?

## もっとべき乗の数字和

Googol ($10^{100}$)は非常に大きな数である: 1の後に0が100個続く. $100^{100}$は想像を絶する. 1の後に0が200回続く. その大きさにも関わらず, 両者とも数字和 ( 桁の和 ) は$1$である.

$a, b \lt 100$ について自然数 $a^b$ を考える. 数字和の最大値を答えよ.

```scheme

(import (scheme base)

        (gauche base))

(define (digit-sum num)

  (assume (exact-integer? num))

  (assume (not (negative? num)))

  (if (zero? num)

    0

    (let loop ([rest num] [result 0])

      (if (zero? rest)

        result

        (loop (div rest 10)

              (+ result

                 (mod rest 10)))))))

(define all-num

  (fold-right (^[n lis]

                (append

                  (map (^m `(,n ,m))

                       (iota 99 1))

                  lis))

              '()

              (iota 99 1)))

(define all-num&digit-sum

  (map (^[lis]

         `(,lis . ,(digit-sum

                     (expt (car lis)

                           (cadr lis)))))

       all-num))

(define max-digit-sum

  (fold (^[result current]

          (if (< (cdr result) (cdr current))

            current

            result))

        '(#f . 0)

        all-num&digit-sum))

(define answer-56

  (cdr max-digit-sum))

(format #t "56: ~d~%" answer-56)

```