3 ms·

> It's just a coincidence that only works in base-10. What? Not at all. In fact, trying it in other bases, as well as with other numbers of digits (in both bas

> It's just a coincidence that only works in base-10. What? Not at all. In fact, trying it in other bases, as well as with other numbers of digits (in both base 10 and other bases), is a useful way to get some insights into why it happens.

krick 3y ago
Yes at all. 6174 is specific to base-10 and 4 digits. For 4 digit numerals in base-9 there are 2 cycles. Same for 4 digit numerals in base-8. It's unlikely that there's any special meaning for 4-digit numbers in base-10 having a single cycle of length 1, but even if there is (possibility which I cannot just deny, of course) — it doesn't translate to other bases. So, yes, the described "special" thing about 6174 is actually a special thing about the string 6174 (representing a number in base-10). And I'd say the fact so many people in this very thread don't understand it is exactly the proof that the GPs comment actually has some merit. People kinda mix up properties of numbers and properties of some other mathematical objects — like their representations in base-10. Most of numerological games are concerned with the latter. Which is why it's especially interesting, when something like that happens to hold in other bases, which sadly just isn't the case with Kaprekar's constant.
- dbrueck 3y ago
  Hehe, to me these contrarian comments are strongly reinforcing my point about overzealous pedantry. :) Of course the specific string '6174' is specific to base 10, but the idea itself can be applied to other bases. Here are some additional examples: dec, 3 digits: 495 hex, 3 digits: 7F8 hex, 30 digits: EECCAA88664421FFDDBB9977553312 dec, 30 digits: 988766544332209987766554332111 hex, 100 digits: FFFFEEEEDDCCCCBBAAAA9998888776666554444333222210FFFFEEDDDDCCCBBBBAA999988777766655554433332211110001 dec, 100 digits: 9999998888888877666666665544444444332222222210999999998877777777665555555544333333332211111111000001 Whether or not things settle on a single number, the number of loops that exist, etc. are a function of the base and the number of desired digits, but in the cases where inputs do settle on a specific number, there are patterns that emerge (regardless of the base) as the number of digits go up.
- codeflo 3y ago
  > And I'd say the fact so many people in this very thread don't understand it is exactly the proof that the GPs comment actually has some merit. Finally someone noticed the irony, thank you. (On the other hand, at least some people also criticize my tone rather than the point I'm making, which I guess is fair as well.)

krick 3y ago

Yes at all. 6174 is specific to base-10 and 4 digits. For 4 digit numerals in base-9 there are 2 cycles. Same for 4 digit numerals in base-8. It's unlikely that there's any special meaning for 4-digit numbers in base-10 having a single cycle of length 1, but even if there is (possibility which I cannot just deny, of course) — it doesn't translate to other bases. So, yes, the described "special" thing about 6174 is actually a special thing about the string 6174 (representing a number in base-10). And I'd say the fact so many people in this very thread don't understand it is exactly the proof that the GPs comment actually has some merit. People kinda mix up properties of numbers and properties of some other mathematical objects — like their representations in base-10. Most of numerological games are concerned with the latter. Which is why it's especially interesting, when something like that happens to hold in other bases, which sadly just isn't the case with Kaprekar's constant.

dbrueck 3y ago
Hehe, to me these contrarian comments are strongly reinforcing my point about overzealous pedantry. :) Of course the specific string '6174' is specific to base 10, but the idea itself can be applied to other bases. Here are some additional examples: dec, 3 digits: 495 hex, 3 digits: 7F8 hex, 30 digits: EECCAA88664421FFDDBB9977553312 dec, 30 digits: 988766544332209987766554332111 hex, 100 digits: FFFFEEEEDDCCCCBBAAAA9998888776666554444333222210FFFFEEDDDDCCCBBBBAA999988777766655554433332211110001 dec, 100 digits: 9999998888888877666666665544444444332222222210999999998877777777665555555544333333332211111111000001 Whether or not things settle on a single number, the number of loops that exist, etc. are a function of the base and the number of desired digits, but in the cases where inputs do settle on a specific number, there are patterns that emerge (regardless of the base) as the number of digits go up.
codeflo 3y ago
> And I'd say the fact so many people in this very thread don't understand it is exactly the proof that the GPs comment actually has some merit. Finally someone noticed the irony, thank you. (On the other hand, at least some people also criticize my tone rather than the point I'm making, which I guess is fair as well.)