6174 — KAPREKAR'S CONSTANT

Pick any four-digit number whose digits are not all identical — leading zeros allowed. Arrange the digits in descending order, then in ascending order, and subtract the smaller from the larger. Repeat the operation on the result. Every starting value in that set reaches 6174, and reaches it in seven steps or fewer. Once there it stays: 7641 − 1467 = 6174.

The result is not obvious and it is not approximate. It is a complete classification of a map on a finite set, proved by exhausting the 8,991 eligible numbers up to permutation of digits, and 6174 is the unique fixed point. D. R. Kaprekar, a schoolteacher in Devlali, India, published it in 1955.

The excluded cases are the ones with all four digits equal — 1111, 2222 and so on — which map straight to 0000 and stay there. Everything else converges. The three-digit version of the same routine has its own constant, 495, reached in at most six steps; most other digit lengths have cycles rather than a single fixed point, which is what makes four digits the memorable case.

This entry is RESERVED, and it is the one reserved number whose print is already decided: the constant set large, with the instruction underneath. It is the cleanest social signal in the queue — an uninitiated reader sees four digits and a dare, and anyone who tries it once remembers the number.