Project Euler

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# [[Problem 4]]

## Largest Palindrome Product

A palindromic number reads the same both ways. The largest palindrome made from the product of two $2$-digit numbers is $9009 = 91 \times 99$.

Find the largest palindrome made from the product of two $3$-digit numbers.

## 最大の回文積

左右どちらから読んでも同じ値になる数を回文数という. 2桁の数の積で表される回文数のうち, 最大のものは 9009 = 91 × 99 である.

では, 3桁の数の積で表される回文数の最大値を求めよ.

```scheme

#!r6rs

#!chezscheme

(import (chezscheme))

(define (RotationNumber? num)

  (let* ([num-string (number->string num)]

         [str-length (string-length num-string)]

         [count (div str-length 2)])

    (let loop ([index 0])

      (cond

        [(<= count index) #t]

        [(equal?

           (string-ref num-string index)

           (string-ref num-string (- str-length 1 index)))

         (loop (add1 index))]

        [else #f]))))

(define (iota-3-digits)

  (filter

    (lambda (n) (<= 100 n))

    (iota 1000)))

(define (make-product-list)

  (let ([i3d (iota-3-digits)])

    (fold-left

      (lambda (lis current)

        (let loop ([result lis]

                   [temp (map

                           (lambda (n) (* n current))

                           i3d)])

          (if (null? temp)

            result

            (loop (cons (car temp) result) (cdr temp)))))

      '()

      i3d)))

(define (make-rotation-number-list)

  (filter RotationNumber? (make-product-list)))

(define answer-4

  (apply max (make-rotation-number-list)))

(printf "4: ~D~%" answer-4)

```