This seems obviously related to the standard manual accounting trick employed when isolating an error in a double ledger - the first thing you do is look to see if the error is evenly divisible by 9. If it is, you've transposed 2 or more numbers somewhere.<p>To prove why this is so:<p><pre><code> For any numbers x and y:
The correct value is 10x + y
The transposed value is x + 10y
The difference is (10x - x) + (y - 10y)
Reduces to 9x - 9y
Factors to 9(x - y)</code></pre>
I don't understand the significance of this at all other than its the coolest thing I've seen on HN in a while.<p>I couldn't be farther from a math nerd.... I avoided it as much as I could throughout school.... but things like that are just so interesting and weird. How on earth (and for what reason) did they find this out? The properties of this number are interesting enough but the process to discover it is just so crazy.
Another interesting four digit number associated with an Indian mathematician is 1729: <a href="https://en.wikipedia.org/wiki/1729_(number)" rel="nofollow">https://en.wikipedia.org/wiki/1729_(number)</a>
That's surprising. Any informal thoughts why would even a single 4-digit constant exist with this property?
The intuition would be there are multiple cycles in this graph.
Reminds me of some cylindrical contraption I saw at the Exploratorium in San Francisco over a decade ago. I believe too it was described even earlier in a "Scientific American" column — either <i>Mathematical Recreations</i> or <i>Computer Recreations</i>.<p>It was some kind of device where a large horizontal cylinder was perhaps covered with numbers? Maybe there were rings or some other kind of "cursor" on the contraption? And I think as you rotated it there was some kind of math performed and, like this "6174" thing, it would seem to converge on a single number after so many iterations regardless of the starting state.<p>Wish I could remember what that was.
6174 is only remarkable if you count in base 10. This is HackerNews, so we all use hexadecimal. Sadly, according to <a href="https://kaprekar.sourceforge.net/output/sample_hex.php" rel="nofollow">https://kaprekar.sourceforge.net/output/sample_hex.php</a>, there is not a simple Kaprekar Constant in base 16.
6174 isn't super special. Or should I say, isn't canonical. It is special but for base 10. But there are other numbers like this for other bases, and of course number lengths.
A rabbit hole into poking around a whole mess of Wikipedia pages about specific numbers, which was pretty entertaining.<p>That said, <a href="https://en.wikipedia.org/wiki/List_of_numbers" rel="nofollow">https://en.wikipedia.org/wiki/List_of_numbers</a> is woefully incomplete.
There’s so much numerology in the world, even among smart people, that I think this is worth being pedantic about:<p>There’s no such thing as a “four-digit number”, only a four-digit <i>base-10 numeral</i>. And facts about base-10 numerals aren’t facts about numbers.