"God's Number" is 20 - Rubik's cube has been "solved"

http://www.cube20.org/

276 61 16 years ago

arnorhs3• 16 years ago

As an amateur speedcuber, I am impressed. Currently I probably use around 100 moves, but my technique is obviously flawed.

Murkin• 16 years ago

Now you have conclusive proof that you are, indeed, not God.

scorpion0322• 16 years ago

He took 5 times the number of steps taken by God. So I propose, a new metric, god index, as the inverse of the number of times of the steps he takes, to the one god would.

His godly index: 20%

greyman• 16 years ago

I am curious, what is so appealing about the speedcubing hobby? Doesn't it become boring and repetitive after some time?

rimantas• 16 years ago

Beating the record (your own or other's) I guess. Canabalt is even more boring and repetitive, but still addictive.

mvarner• 16 years ago

A good friend of mine hangs out with the 7x7 cube champion of the United States. He plays with various different kinds of Rubik's cubes, and from what I gather cubing can also get rather addicting.

teller• 16 years ago

Many speedcubers hit a plateau after a number of years and get bored, true, but it's a deep subject. Every solve is different and there is endless opprotunity for optimization and improvisation. And the physical dexterity aspect just adds to the fun. It would get boring only if you never improved or learned anything new. Definitely more satisfying than Sudoku or Solitaire.

5teev• 16 years ago

I saw a guy solving a cube with only one hand, thus freeing the other hand to do the same thing, more or less.

arnorhs3• 16 years ago

It's the perfect thing to do while you're watching videos or listening to podcasts.

I can't really watch anything or listen to a podcast at the same time that I'm coding. But there is still stuff I really want to watch. This week in startups and some Mixergy shows etc.

But only sitting there watching videos can be very boring, so it's good to have something to do with your hands.

Also. There are so many formulas, techniques, etc. You gradually gain a greater understanding of how the cube works, etc.

I recommend it. Great hobby. But don't be one of those losers that tries to impress a whole party by solving one, it's really lame to cubists.

scorpion0322• 16 years ago

So, your godly index is 0.2 :)

PS: Same here.

jacquesm5• 16 years ago

So, they've brute forced the problem and they now know that there are no positions that need more than 20 moves, but that does not get you closer to developing an algorithm giving you those 20 moves (edit: or however many that configuration takes).

Is there any progress on the algorithmic front?

dan_netwalker• 16 years ago

I'll make an educated guess... the advancement is knowing that if you make a machine that can bruteforce 6 sides x 2 turn directions, you can stop searching once a 20th movement is not enough to get the cube solved, and in the worst scenario, you will check ( 6 x 2 )^20 movements in total. I think that scores as test cases :P

jacquesm5• 16 years ago

Better make that machine of some pretty durable materials then!

randomwalker2• 16 years ago

I think you're confused -- they went the other way around, using the algorithm to find the optimal number.

Search techniques that can quickly solve any cube with a small (near-optimal) number of moves have been known for a while, mainly due to the work of Kociemba: http://www.jaapsch.net/puzzles/compcube.htm#kocal The techniques used are standard AI tree/graph search algorithms with lots of Rubik's cube-specific optimizations.

A few years ago, these methods became good enough to solve almost any cube quickly within 20 moves (which was conjectured to be God's number.) So the algorithm as well as a fast implementation already existed. Here's Kociemba's page http://kociemba.org/cube.htm and here's an iPhone app with a neat twist: you can photograph your physical cube to solve it http://www.wired.com/epicenter/2009/01/iphone-app-solv/

What these guys did was to make further optimizations and run it on a cluster to search through all possible position sets. As they say, they can solve about 4000 positions/s (in 20 moves or less) on a single machine.

jacquesm5• 16 years ago

I re-read the whole article once more, and I think I may be not as confused as you make it out to be.

They explicitly state that they did not generate the optimal number of moves for each of those inputs, only a number <= 20.

So, the question is, does a god-algorithm exist or does it not, and how will this help in finding such an algorithm?

mfukar3• 16 years ago

As far as I can tell, this is simply a (or more appropriately, The) re-discovery of the upper bound on Kociemba's algorithm. The authors apparently did not search for optimal solutions (which is not strictly necessary anyway since we have a lower bound), which you can assume it's equivalent to stopping Kociemba's algorithm when a solution of less than 21 steps is found, for all intents and purposes.

svat• 16 years ago

Discovery, not re-discovery. The upper bound of 20 (that no position takes more than 20 moves) was not known earlier.

Vivtek• 16 years ago

This, and P ne NP on the same day - clearly I can resign my post at the patent office now; everything has already been solved.

elblanco• 16 years ago

Well there you go, I think we're all done here now.

eru3• 16 years ago

Perhaps somebody can still come up with an improvement on the 1-click checkout of Amazon?

noonespecial• 16 years ago

0-click. They decide what I want, send it to me, and then bill me. Pay me.

vog• 16 years ago

0-click. To buy an item, just press the "b" or space key, rather than having to move the mouse to a certain small button and having to click on it.

slig2• 16 years ago

Any guesses of how much this would cost to do on EC2?

fragmede• 16 years ago

Roughly $43000, using spot-instances.

Back of the envelope... From the link, it would take

  1.1 billion seconds @ 4x 2.8ghz
	= 4.4 billion @ 2.8 Ghz
	= 12.32 billion seconds @ 1 Ghz = ~3430000 hours

Using ec2 unit performance as 1Ghz, assume computing is comparable, Ghz for Ghz (it isn't...), and storage and xfer is negligible.

Normal instances

  instance-size|ec2units | $/hr  | $ total
  sm              | 1    | 0.085 | 291550
  large           | 4    | 0.34  | 291550
  xl              | 8    | 0.50  | 214375
  himem-xl        | 6.5  | 0.69  | 364108
  himem-double-xl | 13   | 1.20  | 316615
  himem-quad      | 26   | 2.40  | 316615
  hicpu-med       | 5    | 0.17  | 116620
  hicpu-xl        | 20   | 0.68  | 116620
  cluster         | 33.5 | 1.60  | 163821
  Using spot instances             
  sm              | 1    | 0.031 | 106330
  large           | 4    | 0.14  | 120050
  xl              | 8    | 0.245 | 105044
  himem-xl        | 6.5  | 0.172 | 90763.1
  himem-double-xl | 13   | 0.427 | 112662
  himem-quad      | 26   | 0.871 | 114905
  hicpu-med       | 5    | 0.06  | 41160
  hicpu-xl        | 20   | 0.249 | 42703.5

bd• 16 years ago

With some handwaving it could be about $82.5K (computation spread over 1 year) or $125K (computation done in 1 month).

  total cost was 35 CPU years (Intel Nehalem, 4-core, 2.8GHz)
  1 EC2 compute unit is about 1 GHz Xeon
  let's assume 1 Google unit = 12 EC2 units (3x4 cores)
  High-CPU Extra Large instance = 20 EC2 units

  35*12 = 420 EC2 unit years = 5040 EC2 unit months
  =  21 HiCPU XL instances for 1 year
  = 252 HiCPU XL instances for 1 month

Putting this into AWS calculator [1] yields:

   $82,491.36 (21 HiCPU XL reserved instances for 1 year)
  $125,435.52 (252 HiCPU XL on-demand instances for 1 month)

[1] http://calculator.s3.amazonaws.com/calc5.html

------

Edit: It could be actually a bit more, Nehalems seem to be faster than my first estimate.

Plugging in EC2 computing unit comparison from Cluster Compute instance (which has 2x quadcore Nehalem), 1 Google unit can be 16.75 EC2 units.

This gives:

  $114K for 1 year of 29 reserved HiCPU XL instances
  $166K for 1 year of 18 reserved cluster compute instances

  $173K for 1 month of 348 on-demand HiCPU XL instances
  $246K for 1 month of 210 on-demand cluster compute instances

-----

Edit2: Dedicated server hosting would be much cheaper. For example, from Hetzner [2] it would cost just about 26K EUR (= $34K) to rent 35 dedicated quadcore Nehalem servers for 1 year.

[2] http://www.hetzner.de/en/hosting/produktmatrix/rootserver-pr...

acangiano2• 16 years ago

> With about 35 CPU-years of idle computer time donated by Google, a team of researchers has essentially solved every position of the Rubik's Cube™,

This is the wrong time to use the adverb "essentially". You either solved every position or you didn't.

pohl• 16 years ago

I'd agree with you had they used a weasel-word like "virtually", but "essentially" seems appropriate in this case:

adverb: used to emphasize the basic, fundamental, or intrinsic nature of a person, thing, or situation

If you didn't actually iterate through every position - but rather a subset that provided equivalent coverage by eliminating symmetries - then you have, in essence, solved every position.

acangiano2• 16 years ago

Fair enough. I was in a rush so I didn't read the whole page. Considering their approach, essentially is appropriate.

Avshalom• 16 years ago

Well they didn't actually "solve" every position, they just found a solution under 20 moves for every position.

smallblacksun• 16 years ago

They didn't optimally solve every position, but they did solve every position.

drallison• 16 years ago

Somewhat off point, but the site cube20.org kills Firefox but views OK in Chrome. Firefox reports a seg-fault somewhere.

wazoox• 16 years ago

"works for me", FF 3.6.8 linux 32bits.

rodion_89• 16 years ago

works fine for me on my Linux box in FF 3.6, Opera 10.6, Chromium 6, and (for shits and giggles) in w3m 0.5.2.

ephemient• 16 years ago

It may be the Java plugin crashing when loading the applet. Try disabling it.

JoeAltmaier• 16 years ago

Also proves that all possible cubes are reachable, since they can all be solved.

gojomo• 16 years ago

Hmm... I'm sure someone with more experience will chime in, but I recall reading in a Scientific American years ago that removing a particular piece from the cube then reinserting it wrong could yield a non-solvable configuration.

So I think your statement is only true if you define 'possible' and 'reachable' as synonymous, making it tautological. There are still 'cubes' that look plausible, with the right number of faces of each color and adjacent-faced-pieces, that are still unsolvable.

eru3• 16 years ago

If you disassemble your cube and put it back together, there are 12 possible sets that you can land in. Those sets are not reachable from each other.

The proof is quite elementary.

soundsop• 16 years ago

I see that cube21.org also resolves to the same site, so I guessed they hedged their bets.

rradu• 16 years ago

This is cool and all, but couldn't that computing power have gone to greater use? There is a ton of medical research going on that could have been helped by Google's donation.

"God's Number" is 20 - Rubik's cube has been "solved"

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