# Deceptive puzzle may be solved after 74 years



## qubit (Jun 5, 2011)

> A long-standing and apparently simple puzzle that has left mathematicians stumped for nearly three-quarters of a century may finally be solved.
> 
> The Collatz conjecture was proposed by Lothar Collatz in 1937. It is also known as the "3n + 1 problem" because of its deceptively-simple definition.
> 
> ...



Yeah, it's weird, I tried it and this really works. I wonder how Collatz came up with it?

New Scientist *EDIT:* There's lots of interesting links in the article that don't appear here.

Detailed Wikipedia explanation of the conjecture _This is good for the mathematicians among us and for making regular people's head spin, ie me._


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## Maelstrom (Jun 5, 2011)

That's pretty awesome


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## Funtoss (Jun 5, 2011)

74 YEARS!??? stuff that looool


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## qubit (Jun 5, 2011)

74 years is nothing, dude. There have been mathematical riddles that have been around for hundreds of years. Naturally, I can't think of any off the top of my head, lol.


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## Neuromancer (Jun 5, 2011)

Oh... nm I get it


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## Maelstrom (Jun 5, 2011)

qubit said:


> 74 years is nothing, dude. There have been mathematical riddles that have been around for hundreds of years. Naturally, I can't think of any off the top of my head, lol.



Riemann hypothesis is one (1859). I imagine they are ones that date even farther back.


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## qubit (Jun 5, 2011)

Maelstrom said:


> Riemann hypothesis is one (1859). I imagine they are ones that date even farther back.



Yeah, that was one. I remember reading about a possible proof for it a while back on New Scientist. I take it the proof wasn't, as it would likely make the news if it was.

Here's more headspinning info from Wikipedia on it.


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## twilyth (Jun 5, 2011)

I'm probably wrong about this, but it seems to me that sooner or later, these operations will produce a number that only has 2 as a factor.  In other words, the powers of 2 we are all familiar with - 4, 8, 16, 32, 64, 128, etc.

So if you have an even number and divide by 2 and get an odd number, then 3n + 1 insures that the next number is even.  Eventually, you will get an even number that is a power of 2 and that will necessarily resolve to 1 after repeated divisions.


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## scaminatrix (Jun 5, 2011)

twilyth said:


> So if you have an even number and divide by 2 and get an odd number, then 3n + 1 insures that the next number is even.  Eventually, you will get an even number that is a power of 2 and that will necessarily resolve to 1 after repeated divisions.



Yea, that's what I noticed; it seems kinda ovious that it would *always* get back to zero. Maybe we're too clever for this world 

It essentially boils down to "make an even number out of an odd one and keep halving, then repeat"


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## qubit (Jun 5, 2011)

Scammy, This is true, but the trouble is that this isn't an actual _rigorous proof_ of this. It's frustrating as hell, but until a proof can be formalized, this cannot be said to be true for all cases and any scientific theories based on it, must always come with a disclaimer that this is an assumption!

I've seen mathematical proofs before and they are those complicated confusing things, that I get lost in after only a couple of lines, lol.


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## Kreij (Jun 5, 2011)

It boils down to, "is there a number than when plugged into the formula appears again in the resulting sequence."
If it does you enter an endless loop (infinite stop time) and the conjecture fails.
So far nobody's found one.

Easy little algorithm to code to make some cool graphs and fractals.


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## scaminatrix (Jun 5, 2011)

Ok, -3. If you introduce a negative value, the answer will end up as -1, not 1.

Well, it doesn't mention about having to be a *positive* whole number


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## Maelstrom (Jun 5, 2011)

scaminatrix said:


> Ok, -3. If you introduce a negative value, the answer will end up as -1, not 1.
> 
> Well, it doesn't mention about having to be a *positive* whole number



Yes it does, it says natural numbers, which are only positive integers, not including zero (though it can be included sometimes) https://secure.wikimedia.org/wikipedia/en/wiki/Natural_number


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## scaminatrix (Jun 5, 2011)

I just read the OP, I didn't click the links. Doesn't mention natural numbers there.
You should avoid taking me seriously anyway


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## hat (Jun 6, 2011)

There's a BOINC project about this as well.


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