Taking a numeral core
  (digits: a non-quad four)
      digits I ordered, then
      lesser I minused, till
  evolve I couldn't more.

What is this unfathomably clunky poem all about?


2 Answers 2


You're referring to:

Kaprekar's routine

Quoting from the linked Wikipedia article:
Kaprekar's routine is an algorithm in recreational mathematics which produces a sequence of numbers which either converges to a constant value or results in a repeating cycle. The algorithm is as follows:

1. Choose any natural number $n$ in some base (usually base 10). This is the first number of the sequence.
2. Create a new number $n′$ by arranging the digits of $n$ in descending order, and another new number $n″$ by arranging the digits of $n$ in ascending order.
3. These numbers may have leading zeros, which can be discarded (or alternatively, retained). Subtract $n′ − n″$ to produce the next number of the sequence.
4. Repeat step 2.

For example, if we start with $3524$ then we get:
$$5432 − 2345 = 3087$$ $$8730 − 378 = 8352$$ $$8532 − 2358 = 6174$$ $$7641 − 1467 = 6174$$

A few more points:

- The title refers to the convergence of the number as one of the exit conditions
- The riddle is written in like an algorithm, with the two indented lines representing a loop that is initialized with the line preceding it, and the exit criteria as the line that follows it

And a credit to Florian Bourse's answer for these points:

- Kaprekar's constant is 6174, and each line in the verse consists of words of length 6, 1, 7 and 4.
- The only numbers which when subject to Kaprekar's routine don't converge at 6174 are numbers composed of the same digit (e.g. 1111).
- This ties in to Bass's comment about the poker hand.

  • 2
    $\begingroup$ Everything you say, is of course true, and very much intended. There are a couple of other things I'd really like to see: one is essential for explaining the second line of the poem, and the other one is crucial for saving my reputation as a poet. $\endgroup$
    – Bass
    Commented Mar 19, 2018 at 13:18
  • $\begingroup$ For the second line... is quad referring to a quadruple or quad tuple, to reference the 4 digits? $\endgroup$
    – Phylyp
    Commented Mar 19, 2018 at 13:21
  • 1
    $\begingroup$ I'm not sure if I understand your question, but to remove any ambiguity, the intended meaning of "non-quad four" is "any 4 digits that wouldn't beat a full house as a poker hand" :-) $\endgroup$
    – Bass
    Commented Mar 19, 2018 at 13:31

Building on Phylyp's answer :

All 4 digits numbers except quadruples lead to Kaprekar's constant 6174 when we apply the algorithm described.
Note that each line of the riddle shows words of respectively 6, 1, 7, and 4 letters, reminding us of the fix-point of the algorithm, which makes for the beauty of the riddle.

  • $\begingroup$ Beauty, indeed :-) (and yes, these were exactly the things I meant in my comment to @Phylyp 's answer.) $\endgroup$
    – Bass
    Commented Mar 19, 2018 at 14:35
  • $\begingroup$ Nice - I didn't see the 6-1-7-4 pattern in the verse :-) $\endgroup$
    – Phylyp
    Commented Mar 19, 2018 at 14:50

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.