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 (palindrome? 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]

        [(char=?

           (string-ref num-string index)

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

         (loop (add1 index))]

        [else #f]))))

(define iota-3digits

  (filter

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

    (iota 1000)))

(define 3digits-combinations

  (fold-left

    (lambda (lis current)

      (let loop ([result lis]

                 [temp (map

                         (lambda (n) `(,current ,n))

                         iota-3digits)])

        (if (null? temp)

          result

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

    '()

    iota-3digits))

(define product-3digits-numbers

  (map

    (lambda (lis) (apply * lis))

    3digits-combinations))

(define palindrome-product-3digits-numbers

  (filter palindrome? product-3digits-numbers))

(define answer-4

  (apply max palindrome-product-3digits-numbers))

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

```