Kaprekar’s Constant – Python Challenge

In this challenge, we’re going to explore a fascinating mathematical curiosity known as Kaprekar’s Constant, and then write a Python program to demonstrate how it works.

Kaprekar’s constant, number 6174 has an odd particularity: If you rearrange its four digits in descending order (7641) and take away the number made of these same 4 digits in ascending order (1467) you will fall back on the initial number 7641 – 1467 = 6174!

But that’s not all… The Indian mathematician D. R. Kaprekar discovered something amazing about 4-digit numbers. Here’s the process he found:

1. Take any 4-digit number (at least two different digits).
   Example: 3524

2. Rearrange its digits to create:
   • The largest possible number: 5432
   • The smallest possible number: 2345
3. Subtract the smaller number from the larger one:
   5432 – 2345 = 3087

4. Now take this result and repeat the process!
   Step 1: 5432 – 2345 = 3087
   Step 2: 8730 – 0378 = 8352
   Step 3: 8532 – 2358 = 6174
   Step 4: 7641 – 1467 = 6174

Once you reach 6174, the process stops — because you’ll keep getting 6174 forever!

This number, 6174, is known as Kaprekar’s Constant. No matter which 4-digit number you start with (as long as the digits aren’t all identical), you will always end up at 6174 after a few iterations!

Let’s visualise this with 2025 as our starting 4-digit number:

Python Challenge

The initial challenge is to write a Python program that:

• Asks the user to enter a 4-digit number (with at least two different digits).
• Applies Kaprekar’s routine (rearrange digits, subtract, repeat).
• Displays each step of the process.
• Stops once it reaches 6174.
• Outputs how many iterations it took to reach the constant.

Example output:

Enter a 4-digit number: 3524

Step 1: 5432 - 2345 = 3087
Step 2: 8730 - 0378 = 8352
Step 3: 8532 - 2358 = 6174

It took 3 iterations to reach Kaprekar's constant (6174).

Python Code (Solution)

Extra Challenge

Write a program to count how many iterations it takes for every 4-digit number (from 0001 to 9998) to reach 6174. Use this program to find out both the average (mean) and the maximum number of iterations it takes to reach Kaprekar’s constant amongst all these numbers!

Warning: Make sure to remove any number with the same 4 digits (1111, 2222, 3333… as these cannot lead to Kaprekar’s constant: When applying the process described above on such a 4-digit number, the computer will loop indefinitely without reaching Kaprekar’s constant.

Solution...

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