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  • What is the logic behind Kaprekars Constant?
    Kaprekar's constant, or 6174, is a constant that arises when we take a 4-digit integer, form the largest and smallest numbers from its digits, and then subtract these two numbers Continuing with t
  • Kaprekars constant is 6174: Proof without calculation
    How to prove that by performing Kaprekar's routine on any 4-digit number repeatedly, and eventually we will get the 4-digit constant $6174$ rather than get stuck in a loop, without really calculating
  • Proof of $6174$ as the unique 4-digit Kaprekars constant
    Proof of $6174$ as the unique 4-digit Kaprekar's constant Ask Question Asked 10 years, 4 months ago Modified 5 months ago
  • Mysterious number $6174$ - Mathematics Stack Exchange
    That 6174 is the unique interesting fixed point can be shown without wild and or concrete 'number crunching', cf this recent answer to an older parallel question Would be nice to get your opinion on it
  • sequences and series - Mathematics Stack Exchange
    Why does the kaprekar process of taking a 4 digit number: L, generating L' and L'' such that L' is the digits of L in ascending order and L'' is the digits in descending order and subtracting L' - L'' always converge to the Kaprekar constant of 6174?
  • A strange little number - $6174$. - Mathematics Stack Exchange
    $8730 - 0378 = 8352$ $8532 - 2358 = 6174$ What's more interesting is that with $6174$ we get $7641 - 1467 = 6174$ and taking any four digit number we end up with 6174 after at most 7 iterations A bit of snooping around the internet told me that this number is called the Kaprekar's constant
  • In the Hunt for Kaprekars Constants for more than 4 digits.
    Kaprekar's constant is $6174$ Take any four digit number with at least two different digits; create two four digit numbers by writing the digits in descending order and in ascending order; subtra
  • number theory - Is There Any Solution Of the 6174 Problem . . .
    Here is the relevant Wikipedia article, referenced in the comments The problem is "solved" in the sense that it is easy to check (using a computer) that all 4-digit numbers except repdigits do end up at 6174 On the other hand, it doesn't seem that there is any more satisfying and principled explanation of why this process should end up at the same fixpoint, when this is not the case for 5
  • First level 4-digit numbers (Kaprekar connection)
    The magic number 6174 is a unique four digit number called Kaprekar constant The question is how many first level 4-digit numbers $P_1$ are possible that give $P_1-Q_1=6174 $
  • Non-trivial I know what number youre thinking of
    Write the digits in decreasing order and in increasing order, and subtract the second from the first Repeat $7$ times The result will be $6174$ For example: start with $1234$ $4321 - 1234 = 3087$ $8730 - 0378 = 8352$ $8532 - 2358 = 6174$ $7641 - 1467 = 6174$ (4 times) EDIT: You might also look at some of the answers to this MathOverflow





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