Rubik's Cube Now Solvable in 20 Moves 309
A few years ago we reported that it had been proven that Rubik's Cubes could be solved in 23 moves. Well now that number is
down to just 20. Proving it required 35 years of computer time donated by Google to get it done.
Enough! (Score:5, Funny)
Re:Enough! (Score:5, Funny)
Easy.
Step 1:
Unhook the bra
It's all relative - what do you consider 1 move? I came across this argument during my first DnD session, and subsequently, haven't played it since.
Re:Enough! (Score:4, Interesting)
More and more women are going braless, or are wearing a sports bra. Gone are the days of the hooks.
Re:Enough! (Score:4, Funny)
and the toy, well, I guess you still play with breasts
Yeah, and my mom isn't there to tell me not to put them in my mouth.
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Yes, because chicks dig recursion.
Re:Enough! (Score:5, Funny)
I'm imagining this game session.
You: "Alright, I'll unhook the wood nymph's bra."
DM: "Okay, how do you do that?"
[rest of gaming group listens intently]
You: "Umm...I just, you know, unhook it?"
DM: "Okay, we'll say it takes three rounds."
You: "It doesn't take three rounds to unhook a bra!"
DM: "Well, it takes your character three rounds."
You: "That's bullshit. Have you ever done it?"
DM: "SILENCE! YOU ARE BANISHED FROM DUNGEONS AND DRAGONS FOREVER!"
Re:Enough! (Score:4, Funny)
shouldn't that be
1) unhook bra
2) ???
3) loss (child support, alimony, daycare, etc...)
but step 2 was fun.
Re:Enough! (Score:4, Funny)
You gotta do what I did in 8th grade...find a girl who wanted to learn how to unzip a fly with one hand, and was willing to let you practice taking her bra off with one hand.
I haven't seen her in well over a decade, but I hope her training paid off. I know mine did!
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I'm curious about how that paid off. I've been removing bras two handed for ages now, and it has never been a significant or even minor inconvenience. Maybe it's because I have strong legs?
Re:Enough! (Score:4, Insightful)
I don't think any of them cared that I did it one hand vs two hands...they just cared that I did it quickly. Being able to unhook a bra while having the other hand free to do...uh...other things was nice though :)
Of course, the danger of trying to do it with one hand was if you screwed up or if they had a really wonky bra, suddenly you had to bring your other hand into the equation. That was impossible to do without looking like a moron. If you already started with two hands, that's fine...but if you started with one and ended with two, that meant you thought you were cooler than you actually were -_-;;
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Tip: if true, that girl back then just wanted to get in your fly, you lucky son of a gun. Sorry if the news is a little late
I was fairly oblivious back then... till very much "in-training", lol
Girls have trousers of their own and can practice opening a fly without assistance.
She always said that it wasn't the same when she did it to her own. ::shrug:: I wasn't gonna argue with her, know what I mean?
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Unzipping a fly with one hand is a bit like tying shoes.
You’re an expert at tying shoes? Now go try tying someone else’s shoes.
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Tying someone else's shoes turns out to be pretty easy, as most parents learn. It's a mirror symmetric problem, so it really is functionally the same.
Re:Enough! (Score:5, Insightful)
Tell her to take it off.
Re:Enough! (Score:5, Funny)
Are you kidding? You expect him to talk to a girl?
He actually only needs to know how to unhook a bra because it's currently holding a bundle of Cat6 together.
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Tell her to take it off.
Ask, don't tell.
Re:Enough! (Score:4, Insightful)
Sometimes they like to be told what to do.
This only applies in the bedroom.
In all other circumstances they prefer to be the one telling you what to do.
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You know we also tend to really dislike? Having people assume they know what we want as if we were all the same.
Re:Enough! (Score:4, Funny)
# sudo take it off
Re:Enough! (Score:5, Funny)
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But I haven't programmed in that command just yet!
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Are you new here? This is /. so, it should be listed here [wikipedia.org] :-)
Re:Enough! (Score:4, Informative)
Start with your right arm behind the wearer. Make sure your thumb is on the reinforced section holding the clasp, behind the clasp, on the side to your right. Your index and middle finders should be in a similar position on your left. Squeeze your thumb and the index and middle finger towards each other, while also pressing slightly in (towards you) with your arm. The bra should now be unhooked.
(Lefties use your left hand and switch left and right above.)
Re:Enough! (Score:5, Funny)
That's just unhooking, not removing. Removing in one move is best accomplished through the brute force method. Grab the side opposite the clasp and yank hard.
Re:Enough! (Score:5, Funny)
Placing the hand such that the forefinger is bent against the section of the bra closest to the back and the thumb is over the piece in the foreground with the hooks, slide in the detaching direction with the thumb.
Alternatively, just ask her to take it off for you ... but that may be a problem if you didn't actually know the girl on the bus in the first place.
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I can't speak for every /.'er but I can do with 1 finger in one move. But seriously this is cool.
Zero moves... (Score:2)
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The bras remove themselves after that.
Obligatory XKCD (Score:3, Funny)
Get out of 2names' head, Randall!
http://xkcd.com/457/ [xkcd.com]
Re:Enough! (Score:5, Funny)
Re:Enough! (Score:5, Funny)
You do realize that some of them have FOUR hooks, right? Sure it is easy on the one or two hook models for the smaller chested women. But on the 4 hook models for the larger chested - I defy you to do it with one hand in one "move"...
Bring me a large-breasted woman and I'll show you how it's done!
The exact sequences (Score:5, Funny)
Moves 1 through 19: repeatedly hit cube with hammer
Move 20: reassemble the smashed bits into a solved cube.
Warning: Your cube may or may not remain functional through use of this solution.
Re:The exact sequences (Score:5, Funny)
1) Turn one face 45 degrees
2) Pry upward on one middle edge piece until it pops out
3) Remove all edge and corner pieces
4) Put the cube back together, but flip exactly 1 edge piece
5) Give it to someone who knows how to solve it
6) Laugh maniacally when they just can't seem to get that last piece where it belongs.
Re:The exact sequences (Score:5, Funny)
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Am I mistaken in presuming that you meant “corner piece”, not “middle edge piece”, in step 2?
There is a good reason (Score:5, Interesting)
Another way of thinking about this. (Score:5, Informative)
The shortest path between any two configurations (be them solved or not) on a graph of all possibilities will be no greater than 20.
Re:Another way of thinking about this. (Score:4, Insightful)
As far as I can tell, by simply redefining "solved" any state should be reachable from any other in 20. There's nothing particularly special about all the colours being on the same sides.
1) start from any scrambled state, call it "solved"
2) scramble the cube
3) "solve" in 20 moves.
Laplace Transforms for Rubik's cube... (Score:3, Insightful)
To answer that question, you need to ask whether there is something inherently special about the “solved” state.
Or, to put it differently:
1) Begin in state A
2) Re-arrange stickers into a corresponding state X, such that state A maps directly to state X in a particular transformation system
3) Solve from state X to S (max. 20 moves)
4) Re-arrange stickers using the same transformation system in reverse, obtaining state B, which mapped to state S in that transformation system
Now, if your transformat
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as someone else nicely said. you can name any configuration "solved", so any configuration can then in 20 moves be reconfigured to your solved state
or in your nice notation, say that A = S (or B = S) and you've got your proof?
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Note that the arrangement is not fully arbitrary: there are some arrangements which it is impossible to reach. Not only of the stickers, either (everyone knew that you could make a cube unsolvable by moving the stickers around, right?): it is possible without moving any of the stickers to arrange the pieces themselves in such a way that it is impossible to reach the solved state without taking the cube apart again.
However, among reachable arrangements, your statement is valid. I suspect you probably knew th
That's nothing (Score:2)
I got a team working on solving Rubik's cube in 1 move.
The proof only need 30 years of computering to be proven, however as we only got one computer we won't release is before 2040 (and then we'll claim we were that close to the solution, but due to a timestamp bug we had to restart from scratch in 2038).
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The computer time is necessary to find the move that isn't one of the 12 we usually think of, and will solve any cube.
Schrödinger's solution: (Score:2)
1) Turn the lights off.
The cube now exists in an entangled solved/unsolved state.
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In fact, Schroedinger's cat story was meant to show that quantum physics was just a model, and particles were not really in two different states simultaneously. But most people understood it the wrong way, and now most mentions of the cat experiment promote the oposite idea of what was the initial goal.
35 years of computer time (Score:4, Insightful)
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And considering the processor speeds from 35 years ago, I'm not sure if I would want an application such as this running that long, anyway.
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Except clock-cycles, which is what you get from your equation, is also not a good measurement of "computer usage".
However, Google Tech Talks had a rather nice explanation of the algorithm and core mechanics for solving the problem a couple of years ago. Quite interesting for anyone in supercomputing, or just plain old curiosity.
http://www.youtube.com/watch?v=WQw7c-PliB4 [youtube.com]
Why approximate numbers? (Score:3, Insightful)
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So, they can probably give an upper bound on the number of positions solvable in 20 moves, but not an exact number.
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Re:Why approximate numbers? (Score:4, Informative)
They're counting double moves as one (Score:2, Interesting)
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35 years (Score:2, Funny)
Ok, great.... (Score:2)
Two steps. (Score:2)
Step 1: Remove the stickers.
Step 2: Reapply the stickers,
Graph of Count vs. Distance (Score:2)
Plot the count vs. distance table on a chart and set the count to a log scale. Up to 17 it's almost perfectly linear. I wonder why that is?
-S
How much computing power is this, really? (Score:5, Informative)
35 years is about 300k core-hours, a standard measure of computing resources. This is a big pile of computer time, but is not unreasonable.
So how much does this cost?
A typical supercomputer, Ranger [utexas.edu], cost $59 million to build and operate for four years. It's got about 60k cores, so $59 million delivers 240k core-years; they used 35 core-years to do this computation. Doing the division, you get $9000 of computer time -- not all that bad. Plugging in the cost numbers for another production supercomputer, Kraken [sciencedaily.com], gives a slightly lower cost.
Lower bound = upper bound (finally!) (Score:5, Informative)
Actually, this is a much more important result than the summary claims. Until now, there was always a gap between the proved lower bound and upper bound on necessary moves. They now proved that the known lower bound (20, proved in 1995) is also an upper bound (ie. there is no position which requires 21 or more moves to solve) and thus concluded research that lasted for 30 years.
This article could very well be listed on the Slashdot main page, it has nothing to do in Idle. The algorithms that were designed during this research are nothing to laugh at and will surely advance other research fields as well.
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Re:Thank God! (Score:4, Funny)
Step 2 would be "Not die until step 3", I think.
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Folding@Home [stanford.edu]
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Cancer is unlikely to be cured via brute-force computing. If you've got a computational problem that would help towards a cancer cure, have you asked Google to donate time for it?
Re:Thank God! (Score:5, Informative)
Don't have to, World Community Grid has already been doing cancer cure grid computing for years.
This one is complete:
http://www.worldcommunitygrid.org/research/hdc/overview.do [worldcommunitygrid.org]
These two are still running:
http://www.worldcommunitygrid.org/research/hcc1/overview.do [worldcommunitygrid.org]
http://www.worldcommunitygrid.org/research/hfcc/overview.do [worldcommunitygrid.org]
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If you've got a computational problem that would help towards a cancer cure, have you asked Google to donate time for it?
No, he'd rather just complain. It's much easier to criticize researchers than to do the research yourself.
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Actually, I was at a high-performance physics computing conference this summer in which a genetic oncologist talked about some of the computational challenges in cancer genomics and said, basically, "There's lots of room over here if you physics folks want something else to chew on." It won't be cured by brute-force computing alone, but there are certainly computational challenges where a few million core-hours would be welcome.
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"It's a problem that can't be prevented" and "it's a problem that can't be solved" are two rather different things. So it's caused by undesirable mutations as a result of radiation/chemicals/viruses... doesn't mean we can't fix it once it happens. That being more or less the definition of a cure - a fix you apply to a disease after you already have that disease.
I doubt we'll ever have a vaccine for cancer, for the reasons you mentioned, but a cure... a cure could be achieved.
Although rather than 1 cure fo
Re:Thank God! (Score:5, Insightful)
Yes, you're right, we should devote all our time to getting ourselves to live longer, and none of our time to making our lives more interesting and enjoyable. That'll make a lovely world, won't it.
Re:Thank God! (Score:4, Insightful)
Yes, you're right, we should devote all our time to getting ourselves to live longer, and none of our time to making our lives more interesting and enjoyable. That'll make a lovely world, won't it.
That's what the lifestyle police are pushing for.
Eat food that tastes like cardboard, run like rabbits, and take pills based on how long they'll help you live (never mind quality of life - e.g. so hormone therapy for women is out - can't have 1 more heart attack per hundered even if it makes life bearable for the other 99) and you'll live longer or at least it will feel like it.
Re:Thank God! (Score:4, Insightful)
Yes, you're right, we should devote all our time to getting ourselves to live longer, and none of our time to making our lives more interesting and enjoyable. That'll make a lovely world, won't it.
I agree completely. After watching so many people "live" well past their prime I'd much rather have a good life and a fast death.
Re:Thank God! (Score:4, Interesting)
There's a movement in health research now geared at extending what they call "healthspan" rather than just "lifespan" -- not "how long does this dude keep breathing", but "how long can we keep this dude active and happy"?
Turns out that many of the things that make people live longer also make their late years healthier. My grandfather is 94 and still travels the world with his girlfriend (a spry young 75, but he'll never see her again now that she's taken up Farmville). He got prostate cancer a few years ago (and colon cancer a few decades ago), received aggressive treatment for it, and is now cancer-free and healthy.
Old does not *have* to mean feeble. Sometimes it does, of course, and that's bad; this is why we should look at healthspan rather than lifespan.
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Besides, manually traversing the enormous tree of possible Rubik's Cube states to get to the solution in 20 moves will make any person's life seem much, much longer!
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making our lives more interesting and enjoyable
It appears that you have never watched me attempt to solve a Rubik’s cube.
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When I was about six years old, my cousin challenged me to solve a scrambled Rubik's Cube. The family figured it would keep me busy for hours.
I solved it in the fastest possible way: I pulled off every sticker and put them on the right sides.
Problem solved; it wasn't MY fault they didn't define the problem properly.
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Re:Thank God! (Score:5, Funny)
Thank God!
And cancer? Still unsolved. I'll bet computer time could be used for that too.
It can be shown that a cure for cancer can easily be derived from a method of solving any Rubik's cube in 19 moves.
Re:Thank God! (Score:5, Insightful)
Thank God! And cancer? Still unsolved. I'll bet computer time could be used for that too. (sorry, bullsh*t like this hits very close to home for me recently. Nothing like having people dying, and then hearing how we are using resources for utter crap)
I don't think the limiting factor in cancer research is lack of computer time. If it were something so simple, getting the resources wouldn't be a problem.
Your raging is pointless.
Re:Thank God! (Score:5, Informative)
That's where you are wrong. There is a lack of resources, funding, and computers cycles. There have been cycles running for years. I know cancer researchers, and I've donated time, money, and my computer cycles
While all research could use more funding, cancer research has to be one of the best-funded research fields out there. It's either that or defense. It lacks funding like I lack funding because I can't buy a mansion.
Could you be more specific as to what those cycles were for? I'm guessing they were for protein folding, which is essential and good research but is not going to directly find a cure. If google had run all it's computers on protein folding, we'd likely be only marginally closer to a cure for cancer.
The limiting factor in cancer research is -not- computing time. A bigger one is the fact that there are many different types of cancer, and the biggest one is that it's incredibly difficult to kill millions of any one type of cell without killing a lot of other cells in a human body. For most of our history, we had no idea how to specifically kill bacterial cells in a human body. It's still an issue.
Great job though moderators, bump up misinformation. You'd rage too if you were 34 and had to deal with this shit. And watch, I'll get marked as Troll again, even though I'm not and have a great post history. Whatever.
You're also going to get modded troll because you were asking for it. If you're 34 you should have at some point learned how to calm down and not take things so seriously.
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Does this mean that it was somebody's JOB at Google to figure this out?
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Thank God! And cancer? Still unsolved. I'll bet computer time could be used for that too. (sorry, bullsh*t like this hits very close to home for me recently. Nothing like having people dying, and then hearing how we are using resources for utter crap)
Guess you should be using your spare cycles to help cure cancer. Lead by example instead of using your resources for the utter crap that is posting on slashdot!
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My condolences for your loss, but do you really believe that Google would have found the cure for cancer by now if only they hadn't spent time on this? Big achievements are incremental; someday we might turn this into something bigger or we'll find out it was a waste of time, but it shouldn't be hated simply for being done. How many people here would love to find a way to solve a Rubik's cube in 19 moves? Would you give them the same reaction?
I'm sure this will be difficult coming from someone on the Int
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Oh, they had that for centuries.
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Exactly, but if you use 9 women you get that baby in 1 month!
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Or 1 computer for 1 day if the reference computer is an 8086. Or more likely if you are google, 12,775 computers for 1 day.
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Knowing Google it was probably more like 3500 computers for 3.5 days.
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They started it on an ENIAC emulator and then sped it up according to Moore's Law.
All very proper.
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it was probably 35 CPUs running for a Year. or 70 running for 6 months. article is BS
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From the article (www.cube20.org): "Google does not release information on their computer systems, but it would take a good desktop PC (Intel Nehalem, four-core, 2.8GHz) 1.1 billion seconds, or about 35 CPU years, to perform this calculation."
Maybe read the article next time.
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Obviously the "computer" is one of Google's datacenter machines, which you could equate to a modern enterprise level server. Being too specific doesn't help nearly as much as you think it does. Furthermore:
1 computer running for 35 years = 35 computer years.
35 computers running for 1 year = 35 computer years.
70 computers running for 6 months = 35 computer years.
140 computers running for 3 months = 35 computer years.
420 computers running for 1 month = 35 computer years.
12,600 computers running for 1 day =
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Finally, we were able to distribute the 55,882,296 cosets of H among a large number of computers at Google and complete the computation in just a few weeks. Google does not release information on their computer systems, but it would take a good desktop PC (Intel Nehalem, four-core, 2.8GHz) 1.1 billion seconds, or about 35 CPU years, to perform this calculation.
From the article. They are guessing based on a known configuration how long it would take.