15 Responses to “Mysterious number 6174”
1. John Platonas Jan 16th, 2007 at 2:25 pm
Very fascinating. It never ceases to amaze me how such patterns fall into place.The mathematics in numbers and
what they can produce are like a well organized
syndicate second to none. Extremely clever how this formula seems to always
take us home in this case being 6174.I guess we can say there is no doubt about
it that all roads here do lead to Rome.
2. Speculator Jan 22nd, 2007 at 6:23 am
Perhaps it's the artists signature…
3. Imli Jan 22nd, 2007 at 7:37 pm
Forget about 6174 being a number, but think of it as a collection of digits, with 10 different symbols in 4 spaces —
as if you had a butterfly instead of the 1,
a sweet instead of the 2 etc. It is a very simple process that leads to those
numbers being selected everytime, it has nothing to do with the actual numbers
but everything with what happens in a base n
system to digits and the carry when palindromes are used. In essence you're applying a symmetric rule, and
that of course leads
to stable state eventually.
And what happens when you apply this to the ‘magic number'? Look:
6174 1467 = 4707
7740 477 = 7263
7632 2367 = 5265
6552 2556 = 3996
9963 3699 = 6264
6642 2466 = 4176
6741 1476 = 5265
6552 2556 = 3996
You can immediatly observe that the numbers above to not contain an 8. I'm sure you know that 12345679*8=98765432. So,
what actually happens to 8 here
and why? :)
And for bonus points, do this in hex, or if you are lazy in binary.
4. Daniel Jan 22nd, 2007 at 10:27 pm
“And what happens when you apply this to the ‘magic number'? Look:
6174 1467 = 4707
7740 477 = 7263
7632 2367 = 5265
6552 2556 = 3996
9963 3699 = 6264
6642 2466 = 4176
6741 1476 = 5265
6552 2556 = 3996?
Although I admire your attempt to disprove Matthew's post about Kaprekar's Operation. You didn't take the time to double check your work.
If you were to start with the ‘magic number' as you stated, you would get:
7641 1467 = 6174
7641 1467 = 6174
7641 1467 = 6174
…
as opposed to:
6174 1467 = 4707
This would go on forever, even if you start with the ‘magic number.' Matthew even shows an example of this at the bottom of his first example.
So please, If you are going to try to disprove something that someone else has taken the time to post for us to enjoy, at least double check that you are using the correct rules to do so.
-Daniel
5. DeltaMike Jan 22nd, 2007 at 10:44 pm
Add the results up and they all have the number 9 in common. For example:
6174 - 1467 = 4707 (4 7 0 7=18 then 1 8 = 9)
7740 - 477 = 7263 (7 2 6 3=18 then 1 8 = 9)
6552 - 2556 = 3996 (3 9 9 6= 27 then 2 7 = 9)
etc…
6. Gagan Jan 24th, 2007 at 1:19 am
As Daniel pointed out, Imli did one more mistake, in :
6174 1467 = 4707
7740 477 = 7263
7632 2367 = 5265
6552 2556 = 3996
9963 3699 = 6264
6642 2466 = 4176
6741 1476 = 5265 —–*
6552 2556 = 3996
First mistake is 6174 is not the largest number that can be made out of 6, 1, 7 and 4. but for instance we started with 4707 then what … then too we should get 6174 in the end?.
The mistake is in line *
4176 give 7614-1476 and not 6741-1476.
7. A Mathematician Jan 25th, 2007 at 5:07 am
Further to DeltaMike's observation - any 4 digit number when subtracted in this fashion will be a multiple of 9 - as can be proved easily:
(1000x 100y 10z w) - (1000w 100z 10y x) = (999x 90y - 90z - 999w) = 9(111x 10y-10z-111w) => multiple of nine
Unfortunately, that does not help us arrive at a proof of why 6174 should always be the concluding number
8. Dave Jan 28th, 2007 at 3:48 am
Yeah thanks Mathematician. I hate when egos get in the way of learning. I think this is a great trick and think we should learn more like it, and try to uncover as many mysteries as we can in this life. :)
9. Vox Neo Jan 29th, 2007 at 5:14 pm
Appearantly, the magic number for any series of 3 digits, when treated in the same way, would be 495.
The results for two digit-based numbers will all eventually be sucked in to a one digit, namely 9.
I suppose the same treatment will eventually result in a fixed repetition of results for all thinkable numbers of digits.
(I planned on posting a listing of my own, as a matter of proove, but I don't have enough time at hand, sorry. I will return with a simple pseudo-code listing (and probably a working pascal version) once I figured out how.)
10. Ian Jan 30th, 2007 at 11:52 pm <
Actually, for numbers greater than 4 digits, the Kaprekar series will result in a number of different constants or a repeating loop, but none seem to come down to a single number.
For instance, there are 3 Kaprekar Constants for 10-digit numbers - 9753086421, 6333176664 and 9975084201.
And there are five loops -
8655264432 -> 6431088654 -> 8732087622 -> repeat
8653266432 -> 6433086654 -> 8332087662 -> repeat
8765264322 -> 6543086544 -> 8321088762 -> repeat
8633086632 -> 8633266632 -> 6433266654 -> 4332087666 -> 8533176642 -> 7533086643 -> 8433086652 -> repeat
9775084221 -> 9755084421 -> 9751088421 -> repeat
11. GuilleHate articles like this!!
Maybe he made a mistake is his post, but Imli is right. Mathematics really get interesting when you move beyond these silly tricks with figures and digits, that depend on the particular system being used to represent numbers (in this case, the decimal system).
12.some John Smith Feb 3rd, 2007 at 11:11 am
also: 111,111,111 x 111,111,111 = 12,345,678,987,654,321 :)
13. Another mathematician Feb 9th, 2007 at 12:03 pm
The above is not the whole truth, as there are 77 4-digit numbers that do NOT yeald 6174 as the result of the Kaprekar operation. The original post avoided numbers that contain the same digits (1111,2222, etc), but numbers of the form xxxy, xxyx,xyxx and yxxx where abs(x-y)=1, will fail to produce 6174, because the difference betwene the max and min of such numbers will always yeald 999.
Consider the case xxyx where x = 5 and y = 6, thus 5565
6555-5556 = 999
999-999 = 0
14. Not a mathematician Feb 11th, 2007 at 8:17 am
9990-0999=8991
9981-1899=8082
8820-0288=8532
8532-2358=6174
15. Ron Mar 2nd, 2007 at 7:44 am
While it's 6174 in four-digits, it's 495, also a multiple of 9, in three-digits. (I didn't read all the postings; maybe it's already out there.)
Trying five-digit numbers for a few minutes I seemed to find a cycle that came back to 61974. When divided by 9, it gives 6886. Originally, 6174÷9 gave 686. Fun!
