6174
Take any 4 digit number which has at least 2 digits that are different (e.g. 1112 is OK).
Rearrange the digits to produce the largest possible number and the smallest possible number. Subtract the smaller from the larger one. After at most seven steps, you'll end up with 6174, and then you'll only get 6174 after that. Prove it.
e.g. for 6174 you'd do 7641 - 1467 = 6174
Sadly, this one's easily to find on the Internet, so please don't cheat. I've only looked enough to confirm it's there.
Rearrange the digits to produce the largest possible number and the smallest possible number. Subtract the smaller from the larger one. After at most seven steps, you'll end up with 6174, and then you'll only get 6174 after that. Prove it.
e.g. for 6174 you'd do 7641 - 1467 = 6174
Sadly, this one's easily to find on the Internet, so please don't cheat. I've only looked enough to confirm it's there.
Labels: mathemagic, mathschallenge
posted by Chris at
11:12 PM
5 Comments:
Sadly, on thinking about it, I suspect that this may not have a normal mathematical proof. It's easier to just check every case with a computer.
The number 495 has a similar property for 3 digit numbers.
I'll leave it up because the fact itself is interesting.
1/0.6174 = 1.62 (2D) and = the golden ratio to a tad over 0.1%. But doing it the other way round would say the special number would be 6180.34 approx., so that 6174 is close is just a coincidence.
Not exactly Cam if we take 999 as a four digit number then we have:
9990-0999 = 8990
and if we continue we get to 6174 eventually.
Sorry folks. I should have mentioned that leading 0s might have to be added.
6174 and 495 are the only two numbers that behave like this.
2 => none
3 => 495
4 => 6174
5 => none
6 => 549945 or 631764
7 => none
8 => 63317664 or 97508421
9 => 554999445 or 864197532
10 => 6333176664, 9753086421 or 9975084201
That's all I know (I haven't checked if the 'none's are precise statements.
Much as number problems that are based on decimal representations can me fun/challenging to do, they are not a proper part of number theory. Number theory is independent of decimal etc., reperesentations.
im very confused
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