Cool Trick w/ Numbers

I just heard this, and only checked it for this one case.

1) Write down any 4-digit number*
2) Under that line write the digits from greatest to smallest
3) Under that line write the digits from smallest to largest
4) Subtract line 3 from line 2, this is your new line 1
5) Repeat 2 through 4 as necessary

You will eventually come to the number 6174, which always returns itself. Is this explained anywhere? Are there other numbers for 5-digits?

E.g.
1) 1584
2) 8541
3) 1458
4) 7083

2) 8730
3) 0378
4) 8352

2) 8532
3) 2358
4) 6174

2) 7641
3) 1467
4) 6174


*There are exactly 10 fails to this, and it's when all 4 digits are the same number. E.g. 1111,2222,etc.

Surely you mean 9 fails? unless you're counting 0000 as a 4 digit number.

edit - It's quite interesting that the original operation is actually very restrictive in itself so we aren't really looking at anywhere near 9999 possible numbers due to the fact that 1342 is the same as 4213, etc.

It'd be interesting to see how many numbers churn out 6174 exactly and how many churn out a variation of it.

edit 2 - ignore this link if you actually want to solve it for yourself. Has interesting things 2,3,5,6,etc digit numbers too though and I found the very last big quite interesting too.

http://plus.maths.org/content/mysterious-number-6174

I'd be interested to see if 5 and 7 digit numbers always ended up simplifying down to 9 too, like two digit numbers do.

It sounds like the Collatz conjecture.

Free chocolate

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Originally Posted by jackvance

Free chocolate

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http://i1304.photobucket.com/albums/...ps036408f2.jpg

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Originally Posted by abelardx

It sounds like the Collatz conjecture.

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Hm I'm surprised that this hasn't been proven yet. We should be able to prove that..

Alright well firstly I must say YES it does seem cool, but, it's probably just due to a quirk of our counting system

I used to think it was fascinating how, if you multiplied any number by 9, the result would be numbers that, if summed, would again result in 9.

Examples:

9 x 2 = 81 ; 8 + 1 = 9. Obvious.

9 x 1523456 = 13711104 ; 1 + 3 + 7 + 1 + 1 + 1 + 0 + 4 = 18 ; 1 + 8 = 9. Less obvious.

This is true for any numbers you can think up.

This seemed like a huge number 9 conspiracy to me. But, as it turns out, it can be easily proven that if we used a counting system where we reach say the number 14 before switching over to a second digit (we go from 0 to 9 in a single character, now imagine we went up to 14) the same shit would happen, just with the number 14.

The same result can be generalized to any other number. Since then I've learned that any of these supposed anomalies that come up in numerology are basically a bunch of crap and not worth wasting one's mental energy on.

The best thing about that chocolate video is the bowl full of chocolate next to the bar. It's genius level misdirection

10 internets for everybody! Thanks for the links.

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Oh yeah...

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Originally Posted by Penneywize

Since then I've learned that any of these supposed anomalies that come up in numerology are basically a bunch of crap and not worth wasting one's mental energy on.

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NO, the way YOU have fun is stupid! :p (I'm clearly goofing off, don't hate)

I mean, numerology is a perfect example of when "I don't know" goes to "It must be" with no steps in between. The notion that a number knows how I should spend my time is absurd on so many levels.

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Originally Posted by jackvance

Hm I'm surprised that this hasn't been proven yet. We should be able to prove that..

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why?

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Originally Posted by Luco

The best thing about that chocolate video is the bowl full of chocolate next to the bar. It's genius level misdirection

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I'm still looking for the element that's being swapped out but I still haven't figured it out. :(

OK I figured it out.

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Originally Posted by ImSavy

why?

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Because it seems so intuitively easy. Basically "keep multiplying a number by three and adding one and eventually you'll get a multiple of 2". Idk something with our knowledge of primes should fit in here somewhere. (that said clearly it isn't that easy or it would be solved but it just feels.. solvable)

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Originally Posted by jackvance

Because it seems so intuitively easy. Basically "keep multiplying a number by three and adding one and eventually you'll get a multiple of 2". Idk something with our knowledge of primes should fit in here somewhere. (that said clearly it isn't that easy or it would be solved but it just feels.. solvable)

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People said the exact same thing about Fermat's Last Theorem though. Just because something can be stated in seemingly simple language doesn't imply that it can be solved with the same simplicity.

I could prove it but I don't have enough room here to write it out.

The Collatz conjecture is an Erdos problem. They're all deceptively easy to state.

Ramsey numbers are a perfect example. How many people do you have to invite to a party so that there's always a subset of n people who either all have met before or all haven't met before? For n = 3, the answer is 6. For n = 4, the answer is 18 (hard). For n = 5, no one knows. Finding Ramsey(5) is also an Erdos problem.

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Originally Posted by jackvance

Free chocolate

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I know what I'm doing all weekend.

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Originally Posted by abelardx

The Collatz conjecture is an Erdos problem. They're all deceptively easy to state.

Ramsey numbers are a perfect example. How many people do you have to invite to a party so that there's always a subset of n people who either all have met before or all haven't met before? For n = 3, the answer is 6. For n = 4, the answer is 18 (hard). For n = 5, no one knows. Finding Ramsey(5) is also an Erdos problem.

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I don't get it, shouldn't there be some bayesian probability in there or is it just assumed that every person has either met or not met another with probability 0.5?

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Originally Posted by jackvance

I could prove it but I don't have enough room here to write it out.

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You could have used the margins as well.

Also I think Fermat's Last Theorem was proven finally wasn't it?

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Originally Posted by Penneywize

You could have used the margins as well.

Also I think Fermat's Last Theorem was proven finally wasn't it?

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1995 iirc, which I should as I only read it this morning.

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Originally Posted by Penneywize

I don't get it, shouldn't there be some bayesian probability in there or is it just assumed that every person has either met or not met another with probability 0.5?

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http://en.wikipedia.org/wiki/Ramsey's_theorem

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Originally Posted by Penneywize

I don't get it, shouldn't there be some bayesian probability in there or is it just assumed that every person has either met or not met another with probability 0.5?

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IMO the first person to use the word 'Bayesian' in a conversation wins. :)

http://www.jimloy.com/puzz/missing.htm

:)

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Originally Posted by Penneywize

You could have used the margins as well.

Also I think Fermat's Last Theorem was proven finally wasn't it?

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Yeah I read a book about this ages ago when I got very interested in this illustrous theorem. This one guy shut himself off from the world for years, then came up with a solution, which looked ok upon first peer review.. but turned out to be wrong. So he had to use 7 more years and with the aid of some freshly developed mathematical techniques and he was finally able to prove it. That's from memory and was a long time ago but that was the jest of it I believe.

hmm yes I think you are correct, he did make some error in a critical part of the proof and ended up enlisting some other mathematician dude and appealing to new methods and getting it done. Well, for that he gets immortality, I guess. Though I bet computers will be able to do proofs with little effort, even ones requiring complex / abstract thinking, within the next 20-30 years.

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Originally Posted by Penneywize

hmm yes I think you are correct, he did make some error in a critical part of the proof and ended up enlisting some other mathematician dude and appealing to new methods and getting it done. Well, for that he gets immortality, I guess. Though I bet computers will be able to do proofs with little effort, even ones requiring complex / abstract thinking, within the next 20-30 years.

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Yeah my engineering specialization is in artificial intelligence so I totally adhere to that theory :)

Actually I thought we would be further along already in AI than we currently are, computational power really is an issue, especially now that Moore's Law has apparently reached its boundaries. I'm waiting for quantum computing to make the next big leap (which will have the potential to change everything). There was another big breakthrough last week having done an actual quantum teleportation or something along those lines so I am hopeful.

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Originally Posted by MadMojoMonkey

10 internets for everybody! Thanks for the links.

...

Oh yeah...

NO, the way YOU have fun is stupid! :p (I'm clearly goofing off, don't hate)

I mean, numerology is a perfect example of when "I don't know" goes to "It must be" with no steps in between. The notion that a number knows how I should spend my time is absurd on so many levels.

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Sometimes they end up being trivial, but other times not.

I tried this in base 16 with 4 digits and there are multiple ending points that end up in 4ish number cycles. It's neat that 4 digits decimal works as stated. Maybe I'll extrapolate next week when I'm chillin, aka drinking in my hotel room.

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Originally Posted by jackvance

Yeah my engineering specialization is in artificial intelligence so I totally adhere to that theory :)

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What makes you think this? Is there any examples of AI being capable of any form of rational thought or solving problems or even collecting enough information and using that information to solve trivial problems.

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Originally Posted by ImSavy

Is there any examples of AI being capable of any form of rational thought

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[x] rational
[ ] thought
I wouldn't even consider accusing most humans of rational thought.

There are clearly limits to both our current understanding of what 'mind' is and also what our technology can presently accomplish.

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Originally Posted by ImSavy

solving problems or even collecting enough information and using that information to solve trivial problems.

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As for the other stuff... you're pretty much describing Watson, the computer that beat Jeopardy, right?

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Originally Posted by Penneywize

Alright well firstly I must say YES it does seem cool, but, it's probably just due to a quirk of our counting system

I used to think it was fascinating how, if you multiplied any number by 9, the result would be numbers that, if summed, would again result in 9.

Examples:

9 x 2 = 81 ; 8 + 1 = 9. Obvious.

9 x 1523456 = 13711104 ; 1 + 3 + 7 + 1 + 1 + 1 + 0 + 4 = 18 ; 1 + 8 = 9. Less obvious.

This is true for any numbers you can think up.

This seemed like a huge number 9 conspiracy to me. But, as it turns out, it can be easily proven that if we used a counting system where we reach say the number 14 before switching over to a second digit (we go from 0 to 9 in a single character, now imagine we went up to 14) the same shit would happen, just with the number 14.

The same result can be generalized to any other number. Since then I've learned that any of these supposed anomalies that come up in numerology are basically a bunch of crap and not worth wasting one's mental energy on.

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Maybe not so obvious.... I thought it equalled '18' ???

Kinda cool about the sum of the first & second digits equalling '9'. I'd never thought of it before (& used to be a numbers freak as a kid.. thinking in numbers as opposed to language).