Task — Kaprekar constant

Write a function that takes a 4-digit integer and returns how many iterations are required to reach Kaprekar’s constant (6174). For more information about Kaprekar's Constant please see the Wikipedia page.

Examples

Example 1
Input: $int = 3524
Output: 3
Iteration 1: 5432 - 2345 = 3087
Iteration 2: 8730 - 0378 = 8352
Iteration 3: 8532 - 2358 = 6174

Example 2
Input: $int = 6174
Output: 0

Example 3
Input: $int = 9998
Output: 5
Iteration 1: 9998 - 8999 = 0999
Iteration 2: 9990 - 0999 = 8991
Iteration 3: 9981 - 1899 = 8082
Iteration 4: 8820 - 0288 = 8532
Iteration 5: 8532 - 2358 = 6174

Example 4
Input: $int = 1001
Output: 4
Iteration 1: 1100 - 0011 = 1089
Iteration 2: 9810 - 0189 = 9621
Iteration 3: 9621 - 1269 = 8352
Iteration 4: 8532 - 2358 = 6174

Example 5
Input: $int = 9000
Output: 4
Iteration 1: 9000 - 0009 = 8991
Iteration 2: 9981 - 1899 = 8082
Iteration 3: 8820 - 0288 = 8532
Iteration 4: 8532 - 2358 = 6174

Example 6
Input: $int = 1111
Output: -1
The sequence does not converge on 6174, so return -1.

Analysis

Dattatreya Ramchandra Kaprekar

This is an interesting constant which I don't remember coming across before. Kaprekar was an Indian recreational mathematician who worked as a school maths teacher. He said of himself: 'A drunkard wants to go on drinking wine to remain in that pleasurable state. The same is the case with me in so far as numbers are concerned.'

I can sympathise with that sentiment.

The challenge is easily solved simply by coding the steps given, the only minor issue being the need to left pad a number with fewer than 4 digits with zeroes.

The literature says that the maximum number of iterations required is 7, and 9875 is an example of one that requires 7 steps.

Try it 

#!/usr/bin/perl

# Blog: http://ccgi.campbellsmiths.force9.co.uk/challenge

use v5.26;    # The Weekly Challenge - 2026-01-19
use utf8;     # Week 357 - task 1 - Kaprekar constant
use warnings; # Peter Campbell Smith
binmode STDOUT, ':utf8';
use Encode;

kaprekar_constant(3524);
kaprekar_constant(6174);
kaprekar_constant(9998);
kaprekar_constant(1001);
kaprekar_constant(9000);
kaprekar_constant(1111);

sub kaprekar_constant {
    
    my ($k, $asc, $desc, $n, $explain);
    
    # initialise
    $k = $_[0];
    $explain = qq[$k → ];
    $n = 0;
    
    # repeatedly reverse and subtract
    while ($k != 6174 and $k != 0) {

        # ensure 4 digits
        $asc = substr("000$k", -4, 4);
        
        # sort digits
        $asc = sprintf('%04d', join('', sort(split('', $k))));
        
        # reverse digits and subtract
        $desc = reverse($asc);
        $k = abs($asc - $desc);
        
        # record
        $n ++;
        $explain .= sprintf('%04d', $k) . ' → ';
    }
    
    say qq[\nInput:  $_[0];];
    say qq[Output: ] . ($k ? (qq[$n ∵ ] . substr($explain, 0, -3)) : -1);
}

Output

Input:  3524;
Output: 3 ∵ 3524 → 3087 → 8352 → 6174

Input:  6174;
Output: 0 ∵ 6174

Input:  9998;
Output: 5 ∵ 9998 → 0999 → 8991 → 8082 → 8532 → 6174

Input:  1001;
Output: 4 ∵ 1001 → 1089 → 9621 → 8352 → 6174

Input:  9000;
Output: 4 ∵ 9000 → 8991 → 8082 → 8532 → 6174

Input:  1111;
Output: -1