Magic 1089在使用Dr.racket的方案中

Question

我正在尝试创建一个使用xyz的程序，它的数字按降序排列，并生成1089。我必须取xyz，反转数字，确定xyz和它的反转之间的差异，并称之为diff，加上diff，它就是反转，然后得到1089的答案。我已经尝试了几个小时，但我无法弄清楚如何创建代码。到目前为止，我只尝试了函数，但我仍然不能让它工作。我做错了什么？：

1)

(define h 100)
(define t 10)
(define o 1)

(define (front xyz)
  (number->string (substring xyz 0 1)))

(define (mid xyz)
  (number->string (substring xyz 1 2)))

(define (back xyz)
  (number->string (substring xyz 2 3)))

(define (reversexyz xyz)
  (string->number (+ (* (back xyz) h) (* (mid xyz) t) (* (front xyz) o))))

(define (diff abc)
  (- xyz (reversexyz)))

(define (frontdiff abc)
  (number->string (substring frontdiff 0 1)))

(define (middiff abc)
  (number->string (substring middiff 1 2)))

(define (backdiff abc)
  (number->string (substring backdiff 2 3)))

(define (reversediff xyz)
  (number->string (+ (* (backdiff abc) h) (* (middiff abc) t) (* (frontdiff abc) o))))

(define (magic xyz)
  (+ diff reversediff))

Answer 1

基于this explanation，这应该很简单：

(define (pad0 str) ; add leading 0's to a string, 3 characters wide
  (~a #:width 3 #:align 'right #:left-pad-string "0" str))

(define (reverse-num n) ; reverse a number
  (string->number (list->string (reverse (string->list (pad0 (number->string n)))))))

(define (magic xyz) ; the magic happens here
  (define diff (abs (- (reverse-num xyz) xyz)))
  (+ diff (reverse-num diff)))

测试：

> (magic 123)
1089
> (magic 678)
1089
> (magic 321)
1089
> (magic 546)
1089

FWIW，修改后，仍然有90个数字在100到999 (含)之间，算法不起作用：

> (for/sum ((i (in-range 100 1000)) #:when (not (= (magic i) 1089))) 1)
90