A careful playground for curious numbers

Our educational purpose

Kaprekar.fun explains the mathematical phenomenon discovered by D. R. Kaprekar through clear articles, worked examples, interactive calculators and complete computed datasets. The aim is to help students, teachers and curious readers move from seeing an unusual number trick to understanding the underlying iteration, fixed points and convergence.

What does this site add?

Instead of presenting a single worked example, Kaprekar.fun lets visitors calculate any valid path, compare the three- and four-digit routines, search the complete input space, inspect exact distributions, explore cycles for other digit lengths, and solve a reproducible daily challenge. The explanations and interactive tools are produced specifically for this site.

Who was D. R. Kaprekar?

Dattatreya Ramchandra Kaprekar was an Indian mathematician and schoolteacher known for discoveries in recreational number theory. He presented the four-digit routine associated with 6174 in 1949. His work is the subject of this educational project; the site is not affiliated with his estate or with any academic institution.

How does 6174 work?

Choose any four-digit number containing at least two different digits. Rearrange its digits to make the largest and smallest possible numbers, subtract the smaller from the larger, and repeat. Every valid four-digit input reaches 6174 in at most seven iterations.

What about identical digits?

Repdigits such as 1111 subtract to 0000, then remain there. That is why the accurate claim is about numbers containing at least two distinct digits. Leading zeroes are retained throughout, so an input such as 352 is treated as 0352 in the four-digit routine.

Why is 495 special?

The same routine with three digits converges to 495 for non-repdigit inputs. It is the three-digit sibling of 6174: sorting 495 gives 954 and 459, and 954 − 459 returns 495.

How are the data generated?

The statistics, searchable number list and charts all use the same local calculation engine. For the four-digit view it evaluates every zero-padded input from 0000 through 9999; for three digits it evaluates 000 through 999. Each path continues until a fixed point or repeated state is detected. Nothing is sampled or estimated.

How is accuracy checked?

Automated tests cover standard paths, leading zeroes, repdigits, fixed points and the known 495 and 6174 destinations. Aggregate views are derived from the same tested functions used by the interactive calculator, which prevents the prose, charts and individual results from relying on separate hand-entered datasets.

Beyond 6174

Kaprekar’s routine is the project’s starting point, but the Learn section also covers related ideas: Kaprekar numbers, harshad and self numbers, the Fibonacci sequence, the golden ratio, the Collatz conjecture, happy numbers, digital roots, narcissistic numbers and the 1089 trick. Each article follows the same approach: an original explanation, figures checked by exhaustive calculation, worked examples and links to interactive tools.

Editorial approach

Claims are kept narrow and testable. The site distinguishes mathematical facts from speculation, preserves edge cases instead of hiding them, and cites external references where historical or broader scientific context is discussed. Content is reviewed when functionality or supporting material changes. Last reviewed: 19 September 2026.

Contact

Questions, corrections and privacy enquiries are welcome at info@kaprekar.fun.