[HN Gopher] 6174 ___________________________________________________________________ 6174 Author : gone35 Score : 164 points Date : 2024-01-16 20:35 UTC (2 hours ago) (HTM) web link (en.wikipedia.org) (TXT) w3m dump (en.wikipedia.org) | playingalong wrote: | 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. | Arnavion wrote: | The first reference in the article has the working out. | | https://plus.maths.org/content/mysterious-number-6174 | dcow wrote: | The conclusion is that we don't know and therefore it might | be coincidental. Hardly satisfying. | | It does appear there are cycles for other lengths. | t-3 wrote: | Check out https://en.wikipedia.org/wiki/Kaprekar%27s_routine | | At a glance, there seem to be some patterns, like how for those | bases with a 2-digit Kaprekar number the sum of the digits is | base-1. There must be some number theory explanation for it. | codeflo wrote: | There's so much numerology in the world, even among smart people, | that I think this is worth being pedantic about: | | There's no such thing as a "four-digit number", only a four-digit | _base-10 numeral_. And facts about base-10 numerals aren't facts | about numbers. | recursive wrote: | A lot of numbers have representations in base-10. A fact about | the base-10 digits is a fact about the base-10 representation | of the number, which is also a fact about the number. | | You might be able to satisfy yourself by replacing "the digits | of" with "the decimal digits in the base-10 representation of". | codeflo wrote: | The point is that most of the time when digits are mentioned, | it's only a coincidental fact about one inelegant | representation of the number -- and often people are | insufficiently aware of that. | bee_rider wrote: | Base-10 isn't _in_ elegant, is it? I mean there are good | arguments for 12 being better but it isn't like 10 is prime | or anything. | | Happened across a neat comment yesterday that presents a | defense of ten. Not 100% convinced but it is interesting to | see pushback. | | https://news.ycombinator.com/item?id=39000882 | dr_dshiv wrote: | 1+2+3+4=10 | | And you can swear by that, if you know what I mean. | * * * * * * * * * * | kelnos wrote: | It's only a coincidence if you ignore the fact that "digit" | first and foremost refers to the things sticking out of | your hands, and so was repurposed to talk about numbers | because we have 10 digits on our hands. | shermantanktop wrote: | In some cases, the fact in base-10 has analogous facts in | other bases. A trivial example that adding N-1 to any base-N | number yields a value with the same digit sum. That makes it | a bit more interesting. But I can't think of an example that | doesn't pivot on the representation rather than something | more fundamental. | toxik wrote: | 1+9=10 | semiquaver wrote: | 1 = 1+0 | ChainOfFools wrote: | i'm not sure what you are demonstrating? | | 1 sums digitwise to 1 | | 1 + (10-1) = 10 which also sums to 1 in the same way | shermantanktop wrote: | Right, the digit sum of 10 is 1...perhaps I should have | said "final digit sum." Same for 10000, or 1 with any | number of zeroes after it. | | The point of this trickery is that N-1 added to any | number is really adding N (which adds 1 to the second | position, by definition) and adding -1 (which subtracts 1 | from the first position). | | In base 10, this is the adding 9 trick. It can be | extended by using any multiple of 9. That applies to the | N-1 version, so that adding M*(N-1) to a base N number | yields the same digit sum. | | 1+9 = 10 = 1 | | 1 + 27 = 28 = 10 = 1 | | In hex: | | 1 + F = 10 = 1 | | 1 + 2D = 2E = 10 = 1 | dbrueck wrote: | Eh, I don't know - it doesn't really add much value most of the | time, because these days more or less everyone uses base 10 by | default, so it's entirely reasonable to assume base 10 unless | stated otherwise. | | An argument _against_ being overly pedantic in this case is | that this is a neat and accessible example of something quirky | about numbers, and so even people who don 't know much about | numbering systems can approach it. If you instead emphasize | that it's base 10 or that there is "no such thing as a 4 digit | number", the main thing you'll probably do is cause disinterest | in anyone who is sometimes overwhelmed by math. :) | | Randomly, one of my sons told me about 6174 just a week ago, | and it turned into an interesting conversation following by a | little programming to find more of these numbers. After we went | down that rabbit hole for awhile, _then_ the conversation | shifted to how these numbers might look in e.g. hexadecimal, | and that seemed about the right time for that topic to come up. | selcuka wrote: | > it's entirely reasonable to assume base 10 unless stated | otherwise | | The point of the parent comment is that this is not a | property of numbers in general. It's just a coincidence that | only works in base-10. | | For example, a prime number is prime in every base. An | irrational number is irrational in every base. Collatz | conjecture is valid in every base. This one is not. | ksenzee wrote: | Is there no similar phenomenon for four-digit numerals in, say, | base 8, or base 13? | majewsky wrote: | If you follow the link in the second paragraph to | https://en.wikipedia.org/wiki/Kaprekar%27s_routine, there are | some statements on how this routine plays out in different | bases. For base 8, there is no fixed point with 4 digits | (i.e. any number that immediately loops back to itself), but | apparently there are some cycles (e.g. 3065 - 6152 - 5243 - | 3065). | joehx2 wrote: | > There's no such thing as a "four-digit number", only a four- | digit base-10 numeral | | Being further pedantic - aren't all digits base ten? I thought | that was part of the definition of digit. | | Other bases would have different words for their numbers - bit | in binary, for example (which, yeah, I know, it a combination | of the words "binary" and "digit"). | Anon84 wrote: | If you _really_ want to be pedantic, you say that every base | is base 10 :) (in its own representation) | selcuka wrote: | > Other bases would have different words for their numbers - | bit in binary, for example | | Do we have another example? I don't think there are special | terms for "octal digits" or "hexadecimal digits". | SkyBelow wrote: | While I do personally find tricks involving numbers only in a | specific representation to be worth a bit less, often the | underlying pattern of the trick generalizes into a more | interesting problem. | | For example, per another's link in these comments, this 'trick' | works for 3 digits, but hits 1 of 3 possible loops for 5 | digits. From this, interesting but likely useless questions can | arise, such as finding an easy way to test for these loops, | seeing if there is a way to calculate the loop without brute | forcing it, and understanding the problem enough to know how | much of this holds true when swapping to a new base. | | In general, most of this is just for fun and doesn't lead to | anything serious. But sometimes a fun problem can be hard to | solve, possibly leading to discovering something new, which | ends up being applicable to more serious mathematics. Other | times it can become a trap that just seems to waste time | without ever leading anywhere, like the 3n+1 problem. | | I don't think this should be considered numerology, though I do | think sometimes people treat tricks as if they have some more | serious meaning that they don't deserve, at least not based on | how they are presented. 3 Blue 1 Brown goes into the spiral | pattern of the primes as something that appears to be deep, but | ends up being an unique way to present an otherwise boring | tidbit about prime numbers. | kelnos wrote: | The word "digit" is defined as 0-9, and specifically refers to | base-10. This meaning of the word comes from one of its other | definitions, referring to fingers and thumbs. We have 10 of | those (usually), hence its use as as a reference to the symbols | used in base-10 numbers. | | ("Binary digit" and "hexadecimal digit" are weird terms that | abuse the language a bit.) | Lendal wrote: | It's not really numerology though. Yes it's a dumb trick with | base-10 math but that doesn't make it numerology. It's not | trying to draw any connections between otherwise unrelated | things. I think of numerology as trying to use stupid-glue to | connect things that aren't connected. Like, I was born on the | 8th day of the 2nd month, 8 - 2 is 6, the sixth planet is | Saturn which also has 6 letters, and Jeffrey Epstein's first | pet fish was named Saturn! OMG! That's numerology. | | Numerology is far stupider than this admittedly useless | arithmetic game. | ChainOfFools wrote: | > Like, I was born on the 8th day of the 2nd month, 8 - 2 is | 6, the sixth planet is Saturn which also has 6 letters, and | Jeffrey Epstein's first pet fish was named Saturn! OMG! | That's numerology | | no that's highly opinionated compressionn in the domain of | crazy | epcoa wrote: | Overly specifying a nerdy arithmetic trick will reduce | superstition? If only it were that easy. And properties in a | specific base representation are still properties of the | number. You haven't foiled the numerologist. | dang wrote: | Related: | | _Mysterious number 6174_ - | https://news.ycombinator.com/item?id=2625832 - June 2011 (64 | comments) | | _6174_ - https://news.ycombinator.com/item?id=1625606 - Aug 2010 | (1 comment) | | _Mysterious number 6174_ - | https://news.ycombinator.com/item?id=480200 - Feb 2009 (41 | comments) | Ontol wrote: | it is y combinator | clktmr wrote: | Article says it does work for all numbers except repdigits, but I | think it fails for all palindromic numbers? | mysterydip wrote: | 1221 would become 2211, which avoids the difference becoming | zero. | chasing wrote: | A rabbit hole into poking around a whole mess of Wikipedia pages | about specific numbers, which was pretty entertaining. | | That said, https://en.wikipedia.org/wiki/List_of_numbers is | woefully incomplete. | prvc wrote: | Why do you find this to be significant? ___________________________________________________________________ (page generated 2024-01-16 23:00 UTC)