The Magic Number of Kaprekar

D.R. Kaprekar and 6174

D.R. Kaprekar, an Indian mathematician, discovered a magical property of 4-digit numbers.

The Algorithm

1. Pick any 4-digit number with at least two different digits (e.g., $6382$).
2. Arrange digits in descending order to make the largest number ($8632$).
3. Arrange digits in ascending order to make the smallest number ($2368$).
4. Subtract the smaller from the larger.
5. Repeat with the result.

Flowchart of the Process

Example Walkthrough

Let’s try with $3524$.

1. Digits: $5, 4, 3, 2$.
   • $5432 - 2345 = 3087$
2. Digits from $3087$: $8, 7, 3, 0$.
   • $8730 - 0378 = 8352$
3. Digits from $8352$: $8, 5, 3, 2$.
   • $8532 - 2358 = 6174$
4. Digits from $6174$: $7, 6, 4, 1$.
   • $7641 - 1467 = 6174$ (It repeats!)