Project Euler

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# [[Problem 40]]

## Champernowne's Constant

An irrational decimal fraction is created by concatenating the positive integers:

$$0.12345678910{\color{red}\mathbf 1}112131415161718192021\cdots$$

It can be seen that the $12$<sup>th</sup> digit of the fractional part is $1$.

If $d_n$ represents the $n$<sup>th</sup> digit of the fractional part, find the value of the following expression.

$$d_1 \times d_{10} \times d_{100} \times d_{1000} \times d_{10000} \times d_{100000} \times d_{1000000}$$

## チャンパーノウン定数

正の整数を順に連結して得られる以下の10進の無理数を考える:

$$0.12345678910{\color{red}\mathbf 1}112131415161718192021\cdots$$

小数第12位は1である.

$d_n$ で小数第$n$位の数を表す. $d_1 \times d_{10} \times d_{100} \times d_{1000} \times d_{10000} \times d_{100000} \times d_{1000000}$ を求めよ.

```scheme

(import (scheme base)

        (gauche base)

        (scheme flonum))

(define (digit-of-num n)

  (assume (exact-integer? n))

  (assume (<= 0 n))

  (if (zero? n)

    1

    (+ (floor->exact (fllog10 n))

       1)))

(define (number-list n)

  (assume (exact-integer? n))

  (assume (<= 0 n))

  (if (zero? n)

    '(0)

    (let loop ([rest n]

               [result '()])

      (if (<= rest 0)

        result

        (loop (div rest 10)

              (cons (mod rest 10)

                    result))))))

(define (champernowne d)

  (let ([result (make-vector (+ d

                                (digit-of-num d)

                                1))])

    (let loop1 ([current 1] [pos 1])

      (if (< d pos)

        result

        (let loop2 ([count (digit-of-num current)]

                    [numlis (number-list current)]

                    [pos pos])

          (cond

            [(<= count 0)

             (loop1 (+ current 1) pos)]

            [else

              (vector-set! result pos (car numlis))

              (loop2 (- count 1)

                     (cdr numlis)

                     (+ pos 1))]))))))

(define answer-40

  (let ([cn100_0000 (champernowne 100_0000)])

    (* (vector-ref cn100_0000 1)

       (vector-ref cn100_0000 10)

       (vector-ref cn100_0000 100)

       (vector-ref cn100_0000 1000)

       (vector-ref cn100_0000 1_0000)

       (vector-ref cn100_0000 10_0000)

       (vector-ref cn100_0000 100_0000))))

(format #t "40: ~d~%" answer-40)

```