Project Euler

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

# [[Problem 52]]

## Permuted Multiples

It can be seen that the number, $125874$, and its double, $251748$, contain exactly the same digits, but in a different order.

Find the smallest positive integer, $x$, such that $2x$, $3x$, $4x$, $5x$, and $6x$, contain the same digits.

## 置換倍数

125874を2倍すると251748となる. これは元の数125874と順番は違うが同じ数を含む.

2x, 3x, 4x, 5x, 6x が x と同じ数を含むような最小の正整数 x を求めよ.

```scheme

(import (scheme base)

        (gauche base))

(define (number->list num)

  (assume (exact-integer? num))

  (assume (<= 0 num))

  (if (zero? num)

    '(0)

    (let loop ([rest num] [lis '()])

      (if (zero? rest)

        lis

        (loop (div rest 10)

              (cons (mod rest 10)

                    lis))))))

(define perm-num?

  (case-lambda

    [(num1 num2)

     (let ([num-list1 (number->list num1)]

           [num-list2 (number->list num2)])

       (if (not (= (length num-list1)

                   (length num-list2)))

         #f

         (let loop ([rest-1 num-list1]

                    [rest-2 num-list2])

           (cond

             [(null? rest-1) #t]

             [(find (cut = <> (car rest-1))

                    rest-2)

              (loop (cdr rest-1)

                    (delete (car rest-1) rest-2))]

             [else #f]))))]

    [(num1 num2 . num3)

     (and (perm-num? num1 num2)

          (apply perm-num? num2 num3))]))

(define find-6digit

  (let loop ([num1 102345])

    (if (< 165987 num1)

      (errorf "解が見つかりませんでした~%")

      (let ([num2 (* num1 2)]

            [num3 (* num1 3)]

            [num4 (* num1 4)]

            [num5 (* num1 5)]

            [num6 (* num1 6)])

        (if (perm-num? num1 num2 num3 num4 num5 num6)

          num1

          (loop (+ num1 1)))))))

(define answer-52 find-6digit)

(format #t "52: ~d~%" answer-52)

```