Project Euler

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# [[Problem 30]]

## Digit Fifth Powers

<p>Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:

\begin{align}

1634 &= 1^4 + 6^4 + 3^4 + 4^4\\

8208 &= 8^4 + 2^4 + 0^4 + 8^4\\

9474 &= 9^4 + 4^4 + 7^4 + 4^4

\end{align}</p>

As $1 = 1^4$ is not a sum it is not included.

The sum of these numbers is $1634 + 8208 + 9474 = 19316$.

Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.

## 各桁の5乗

<p>驚くべきことに, 各桁を4乗した数の和が元の数と一致する数は3つしかない.

\begin{align}

1634 &= 1^4 + 6^4 + 3^4 + 4^4\\

8208 &= 8^4 + 2^4 + 0^4 + 8^4\\

9474 &= 9^4 + 4^4 + 7^4 + 4^4

\end{align}</p>

ただし, $1 = 1^4$ は含まないものとする. この数たちの和は 1634 + 8208 + 9474 = 19316 である.

各桁を5乗した数の和が元の数と一致するような数の総和を求めよ.

```scheme

(import (scheme base)

        (gauche base))

(define (fifth-power n)

  (fold (^[n acc]

          (+ (expt n 5) acc))

        0

        (map (cut digit->integer <>)

             (string->list (number->string n)))))

(define fifth-power-list

  ; (* (expt 9 5) 6) -> 354294

  ; (* (expt 9 5) 7) -> 413343

  ; なので、2 ～ 354294 まで求めればよい

  (map (^n (cons n (fifth-power n)))

       (iota 354293 2)))

(define digit-fifth-powers

  (map (cut car <>)

       (filter (^c (= (car c) (cdr c)))

               fifth-power-list)))

(define answer-30

  (apply + digit-fifth-powers))

(format #t "30: ~d~%" answer-30)

```