Kaprekar's Constant
Updated 2026-08-03
INTRODUCTION
English translation pending.
CORE DEFINITION
Discovered by Indian mathematician D. R. Kaprekar. Take any four-digit number whose digits are not all identical, arrange the digits in descending and ascending order, subtract the smaller from the larger, and repeat. The process reaches 6174 within at most seven iterations and then cycles there forever. The constant is an attractor of the iteration rule: it depends on the arithmetic and the base-ten representation, not on the starting value. The requirement that digits not all be identical matters, since such inputs collapse immediately to zero.
SCAFFOLDING EFFECT
Reduce cognitive load
- Convergence reading: ask whether your system has a fixed point that all trajectories reach regardless of starting position. - Initial-condition skepticism: check whether early advantages matter once the rule has run for several rounds. - Rule design: recognize that changing the iteration rule changes the attractor, not the starting point.
Anchor fast decisions
The subtraction step sorts digits and cancels their positional contributions, so information about the original arrangement is destroyed each round. After a few iterations the state space collapses to a small set of values, and 6174 is the fixed point of that reduced set. The outcome is therefore a property of the operation, which is why wildly different starting numbers converge on the same endpoint.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
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Source support: Explicit
- en.wikipedia.orghttps://en.wikipedia.org/wiki/Kaprekar's_routineverified
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