Kaprekar's constant
Let an agent define the Kaprekar routine and constant precisely, run the routine on a given number, state the conditions and the corresponding constants for other digit lengths, and distinguish the constant from Kaprekar numbers.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Define The routine and constant.
Routine
The routine.
Routine
Routine.
- How does the Kaprekar routine work, and what inputs are allowed? definition
- Is the question about the constant 6174 or about Kaprekar numbers? boundary
Constant
The constant.
Constant
Constant.
- Why is 6174 a fixed point, and why does every valid input reach it? definition
- Which entry fits fixed points generally? action
Compute Running the routine.
Run
Running.
Run
Run.
- What sequence does a given number produce, and in how many steps? action
- What is the result for the number in question? measurement
Bound
Step bound.
Bound
Bound.
- How is the seven-step bound established? provenance
- Which references are standard? provenance
Generalise Other lengths and bases.
Lengths
Other digit lengths.
Lengths
Lengths.
- What happens for three, five and more digits, and which produce constants or cycles? provenance
- Which entry fits the three-digit constant? action
Bases
Other bases.
Bases
Bases.
- What is known about the routine in other bases? provenance
- What is proven versus computed? boundary
Context History and teaching.
History
Kaprekar.
History
History.
- Who was Kaprekar, and how did he find the constant? provenance
- Which entry fits the person? action
Teach
Teaching.
Teach
Teaching.
- How is the constant used in teaching and puzzles? action
- Which misconceptions arise? provenance
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QTY
What it is Filled
The number 6174, the fixed point of the Kaprekar routine on four-digit numbers: take any four-digit number with at least two different digits, arrange its digits in descending and ascending order, subtract the smaller from the larger, and repeat; the process reaches 6174 within at most seven steps and then stays there, a result found by D. R. Kaprekar in 1949.
Why it exists Filled
Let an agent define the Kaprekar routine and constant precisely, run the routine on a given number, state the conditions and the corresponding constants for other digit lengths, and distinguish the constant from Kaprekar numbers.
Distinguishing features Filled
- Fixed point of a digit-sorting subtraction routine
- Universal for four-digit inputs with two distinct digits
- Bounded number of steps
- No single constant for most other lengths
What robots and AI may and may not do Filled
Must not
- Forget the condition that the number has at least two different digits.
- Drop leading zeros in a way that breaks the routine.
- Confuse Kaprekar's constant with Kaprekar numbers.
- Present the constant as having uses it does not have.
Only with a human decision
- Using the routine in assessed teaching where errors carry marks.
May
- Run the Kaprekar routine on a four-digit number and show each step.
- Explain why 6174 is the fixed point.
Moral aspects Filled
- Mathematical curiosities are often padded with false claims; accuracy keeps trust.
Who is affected
- Learners and puzzle readers
- Teachers
Owners Filled
Steward
Nobody owns the concept; it belongs to the shared body of mathematics.
Links to other meta-models Filled
parent
- Q217608 - registry parent class
- Q28920052 - registry parent class
related
- fixed point - of the Kaprekar routine
- Kaprekar routine - the procedure
- Kaprekar number - a different property
- On-Line Encyclopedia of Integer Sequences - sequence A099009 for fixed points
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.kaprekar-s-constant
- Wikidata: Q854503 (https://www.wikidata.org/wiki/Q854503)
- OEIS: A099009 fixed points of the Kaprekar map
Direct properties not applicable Not applicable
- value: 6174 integer
- maximum steps: 7 iterations - for four-digit inputs
- three-digit constant: 495 integer
Plane XCT: no invented physical properties.
Recognition optional Filled
- Fixed point of the four-digit Kaprekar routine
- Reached within seven steps from any valid start
- Kaprekar numbers such as 45 are a different notion
- Not visible; the number 6174.
Capabilities and actions required Filled
- run the routine on a given number
- state the conditions and step bound
- relay constants for other digit lengths
- distinguish the constant from Kaprekar numbers
Hazards and failure modes required Filled
- Forgetting the two-distinct-digit condition
- Dropping leading zeros incorrectly
- Confusing with Kaprekar numbers
Standards and interfaces required Filled
- No regulation; definitions follow the literature
Context of use required Filled
- Not for anything; a curiosity in recreational mathematics.
- the four-digit constant 6174
- the three-digit constant 495
- cycles rather than constants for other digit lengths
- Kaprekar routine in other bases
Sources Filled
- Wikidata item Q854503: Kaprekar's constant - identity and sense of the item
- Wikipedia: Kaprekar's constant - general description of the item
Open questions
- Should the Kaprekar routine be a separate entry?
- How should OEIS entries be linked?
- How should results for other bases be recorded?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q854503/spec.json