That got me thinking. The rational numbers, I mean.
Then Kaprekar came into mind. Indian guy who loved to play with the integers.
Try this: pick any 4-digit number (digit - a single numeral), make the largest and the smallest number you can from the four digits available ( make sure the digits are mainly different). For example - choose 3298, the largest new number you can get by juggling is of course, 9832. The smallest is 2389. NOW, subtract the smaller from the larger and you get a new one - namely, 7443. Use this number to continue forthwith; Namely, 7443 - 3447 = 3996 etc.
It always stops at 6174.
You tell me.
For three digits it is always 495. After four digits, the process cycles, but for three and four digits, it ALWAYS ends in 495 and 6174, respectively.
One has to ponder what other significance these two otherwise unimpressive integers have, if any. And how many others there are out there, if only we ask the right questions.
For those of you who are more of the inquiring nature, try a similar exercise called the "Goldbach Conjecture" ~ to be elaborated on in a future post.
If I ever buy a house in a long street, I want the house number to be either 495 or 6174. I regard these numbers as the opposite to "13" (for the English among you), or "4", (for the Koreans among you), or "42" (For the pessimists among you, Koreans or otherwise).
Mathematics was not one of Douglas Addams' strong points.
Tuesday, April 12, 2005
What is special about 6174?
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3 comments:
unlike other special numbers you've mentioned in some of your other posts, like pi and e, it is not the value of this number which is signficant, but rather, its base10 representation.
we can see that 6174 works:
7641 - 1467 = 6174
converting 6174 to base16 we get:
181E
well, right there we see that the digit "1" is repeated, which is a little against the rules, but lets try it anyway:
E811 - 118E = D683
so we can see that that did not work. converted back into base10, D683 is 54915, so that isn't anything significant either.
but, again, the number 181E broke the repeated digit restriction anyway, so let's try converting 6174 to base8 instead:
14036
does this number work? let's try again:
64310 - 01346 = 62742
nope, still doesn't work. therefore, i do not believe that there is much more significance to the number 6174 and 495 than what you have already mentioned.
Lancelot, of course I have known it is only the base that makes this possible.
It is interesting that you chose the more complicated one to test it, though.
If I were testing, I would have used 495!
of course, i knew that you knew, miss geisha, because i know you are smarter than me. if i had written an email to you about it, if would have probably just said, "eh, it's only like that because of the base10 representation so i don't really find myself pondering any other significances."
but i was making a blog post, so i thought i'd be a bit more demonstrative. :) and also use the title number!
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