Sunday jugglers: solves Rubik’s cube while juggling, another juggler plays the piano

Like everyone else, I once had a Rubik’s cube (the world’s best-selling toy, 350 million of them had been sold by 2009), but I am simply puzzle-illiterate, and gave it up quickly. This video puts me to shame.

Via Vibe, we have this amazing video of Stanford student Ravi Fernandez (dubbed “Sir Ravi” by his worshipful friends) solving one Rubik’s cube while juggling three of them. See if you can watch him move the squares while the cube is in his hand.

It’s no wonder I couldn’t solve it. As Wikipedia notes:

The original (3×3×3) Rubik’s Cube has eight corners and twelve edges. There are 8! (40,320) ways to arrange the corner cubes. Seven can be oriented independently, and the orientation of the eighth depends on the preceding seven, giving 3^{7} (2,187) possibilities. There are 12!/2 (239,500,800) ways to arrange the edges, since an even permutation of the corners implies an even permutation of the edges as well. (When arrangements of centres are also permitted, as described below, the rule is that the combined arrangement of corners, edges, and centres must be an even permutation.) Eleven edges can be flipped independently, with the flip of the twelfth depending on the preceding ones, giving 2^{11} (2,048) possibilities.

which is approximately forty-three quintillion.

The puzzle is often advertised as having only “billions” of positions, as the larger numbers are unfamiliar to many. To put this into perspective, if one had as many standard sized Rubik’s Cubes as there are permutations, one could cover the Earth’s surface 275 times.

As lagniappe, here’s another remarkable juggler: Daniel Menendez, who plays the piano while juggling (there are more recent clips of him on YouTube, too). Be sure to watch it to the end to see the Grand Finale. And don’t forget to tip the waitress!

He isn’t playing the piano, he’s simply dropping the balls onto a board that is coded to produce the music as each ball hits it. All it needs is some simple programming, and the ability to juggle the four balls.

I agree. I was following the balls and they do not hit the keys correctly as I would expect for real play. The piano is pre-programmed to play notes just when you hit any of the key. I would not be surprised if the piano is not the piano but just a board sensitive to ball hits with painted key on it.

Truly extraordinary. The only way I’ve ever managed to impress anyone with a Rubik’s Cube was thanks to the fact that I was one of the first people to buy one – I could show it to my friends, who had never seen one. After months of practice I got to the stage where I could reliably solve it in under five minutes, but that was as far as it went. (And I’ve long since forgotten how to do it.)

Pragmatically, I’m sure it helps that he can clearly distinguish the cube which he’s solving from the balls he’s also juggling. If he was juggling three cubes while solving one I expect confusion could arise.

Having said that, it is still very impressive indeed.

Interestingly, a Stanford professor of genetics cracked Rubik’s cube in 4 hours realizing that an underlying key to unlocking the puzzle would be the mathematics of group theory, also used in genetics (not to mention crystallography).

The basic key is to find move sequences of the form A B A’ B’, where A and B are different series of moves and A’ is just doing A backwards, and so with B’ and B. This does not get you back to where you started (you would have to do A B B’ A’ to get back where you started), but it does leave you having impacted only cubes that overlap both the A sequence and B sequence.

I can’t claim to have worked out a solution to the cube by myself back in the – late 70s/ early 80s, wasn’t it?
But I did cotton onto the A B A’ B’ concept that you mention, though I couldn’t have expressed it so succinctly. For the solution sequence that I know, that specific trick occurs twice (arranging the edge pieces of the final face, and re-arranging corner pieces).
I got a 3-cube again a couple of years ago after 25 years without one. It took a couple of hours for the “muscle memory” to come back, and another couple of hours to get back up to a typical 2-minutes for a solution. I was never terribly fast, because I can only rarely see 2 moves in advance.
Despite the quadrillions of solutions, there are only a small number of steps to a general solution:
(1) solve 1 face, including the edge pieces being in order; (2 sets of moves, including an ABA’B’ pattern);
(2) solve the edges on the next layer; (one set of moves, repeated 2 to 6 times);
(3) solve the edges of the final layer; (one move set, once or twice, rarely thrice ; sets can be run together into ABA’B’ sets, saving several moves);
(4) arrange the bottom layer corners into the correct places (ABA’B’ move set, once or twice, depending on how well you can read ahead)
(5) rotate the bottom layer corners in place (more A B A’ B’ sets, two or three times, four if you read the initial configuration wrongly).
Which is all very well and good. I got a 4-cube at the same time, and still can’t work out how to solve that.

Jerry, I noticed you have used lagniappe twice in the last week. It’s nice to see that one of our less common Gulf coast words is making its way northward.

I knew a kid in high school that could solve a Rubik’s cube behind his back while jumping on a pogo stick. People would bring him their own cubes, would mix the cubes up themselves, and then he’d jump on and go to work. Basically, he would find one cube (in the cube), keep track of it with his thumb, and finish the rest of it via mental mapping. He was pretty entertaining to watch.

His actual name is Ravi Fernando, a math student from Missouri, not Fernandez. He is juggling in front of the bookstore which is a fairly popular spot for Stanford jugglers (Down with Gravity, late Friday afternoons). When not juggling he can apparently solve a cube in about 10 seconds.

BTW he also got 8th in the 2011 Putnam Competition.

Solving a Rubik’s Cube is incredibly easy once you know how. You don’t even have to look at the thing except to see the starting position on one side. Once you know that, the speed of solving the cube is based only on how fast you can turn the sides. When I was in high school I could solve the cube in about 20 seconds with my eyes closed. Admittedly I found the solution in a book and didn’t solve it on my own, but I sure impressed the hell out of people.

I would bet very few (probably none) of the speed solvers of the rubiks cube actually solved it on their own. I read the solution myself. Basically it’s a memorization of moves based on pattern. I never memorized the complete pattern. I solve the first layer brute force first, which is easy. Then the 2nd layer is solved by applying memorized pattern after trying to put the cubes in certain patterns. The last layer is purely solved by memorized sequence of moves.

My brother and his friends worked on speed solving. I made patterns. Now I have three cubes, one normal, one with a twisted corner and one with two sides reversed so I can get patterns that are not available on a regular cube. I also have 2 x 2, 4 x 4 and 5 x 5 cubes. Eventually I will splurge and get the 6 x 6 and 7 x 7 cubes just to see what patterns I can make on those..And I cannot juggle worth a damn!

The “Piano Juggler” is not playing a piano or a keyboard in any sense. He isn’t. Sorry!!! Unless you mean something like a keyboard where you press one key and a whole melody comes out. Very impressive, not.

Though he seems like a nice enough fellow and he certainly wants to entertain the crowd from a good heart. So that’s a good thing.

I’d be amazed seeing a video of an actual concert pianist who can juggle. Or solve a scientific problem of any sort :-)

Well, in a more recent thread, Dr. Coyne shows a video of Harvard math professor Tom Lehrer, who is quite a decent pianist (and competent vocalist, composer and lyricist). Does that qualify?

Oh, and I am a concert pianist, and I can juggle (the juggling part is reasonably easy, the piano playing is quite a bit more difficult).

Here’s a female engineer/concert pianist/Rhodes Scholar:

I doubt seriously that I could solve the Rubik’s cube today, but when I was a teenager, I regularly managed to get it back into its correct position within just a few minutes.

It was extremely easy. Anyone who wasn’t able to do so has a serious mental deficiency.

All you need to do is to take an ordinary kitchen knife and lever one of the pieces out. The remainder of the cube can then be easily disassembled and reassembled into the correct position.

The other way I did it was that I bought a book explaining how it was done, which I then modified. From memory, I realized that once I got one face correct, the remainder almost seemed to solve itself.

Something I always regarded as being quite as remarkable as the complexity of the puzzle itself, was how the damn thing was made. Contemplate the problem of how to make three rows of squares slide past each other in any one of three planes, and the answer is not at all intuitive.

## 26 Comments

He isn’t playing the piano, he’s simply dropping the balls onto a board that is coded to produce the music as each ball hits it. All it needs is some simple programming, and the ability to juggle the four balls.

I agree. I was following the balls and they do not hit the keys correctly as I would expect for real play. The piano is pre-programmed to play notes just when you hit any of the key. I would not be surprised if the piano is not the piano but just a board sensitive to ball hits with painted key on it.

Wow! The odds of solving a Rubik’s cube must be like the odds of a tornado blowing through a junkyard and assembling a 747!

That is to say, the board is a sequencer, and the only thing he controls during the performance is the rhythm.

http://pogue.blogs.nytimes.com/2007/01/02/too-good-to-be-real/

It’s still pretty cool!

I don’t want to know how he juggles the balls and get the tunes, all I know he is awesome at it!

Truly extraordinary. The only way I’ve ever managed to impress anyone with a Rubik’s Cube was thanks to the fact that I was one of the first people to buy one – I could show it to my friends, who had never seen one. After months of practice I got to the stage where I could reliably solve it in under five minutes, but that was as far as it went. (And I’ve long since forgotten how to do it.)

Pedantically, I think Sir Ravi is juggling two balls and one cube, rather than three cubes?

And, no, I don’t think that detracts from his awesomeness one iota!

Pragmatically, I’m sure it helps that he can clearly distinguish the cube which he’s solving from the balls he’s also juggling. If he was juggling three cubes while solving one I expect confusion could arise.

Having said that, it is still very impressive indeed.

Interestingly, a Stanford professor of genetics cracked Rubik’s cube in 4 hours realizing that an underlying key to unlocking the puzzle would be the mathematics of group theory, also used in genetics (not to mention crystallography).

The basic key is to find move sequences of the form A B A’ B’, where A and B are different series of moves and A’ is just doing A backwards, and so with B’ and B. This does not get you back to where you started (you would have to do A B B’ A’ to get back where you started), but it does leave you having impacted only cubes that overlap both the A sequence and B sequence.

I can’t claim to have worked out a solution to the cube by myself back in the – late 70s/ early 80s, wasn’t it?

But I did cotton onto the A B A’ B’ concept that you mention, though I couldn’t have expressed it so succinctly. For the solution sequence that I know, that specific trick occurs twice (arranging the edge pieces of the final face, and re-arranging corner pieces).

I got a 3-cube again a couple of years ago after 25 years without one. It took a couple of hours for the “muscle memory” to come back, and another couple of hours to get back up to a typical 2-minutes for a solution. I was never terribly fast, because I can only rarely see 2 moves in advance.

Despite the quadrillions of solutions, there are only a small number of steps to a general solution:

(1) solve 1 face, including the edge pieces being in order; (2 sets of moves, including an ABA’B’ pattern);

(2) solve the edges on the next layer; (one set of moves, repeated 2 to 6 times);

(3) solve the edges of the final layer; (one move set, once or twice, rarely thrice ; sets can be run together into ABA’B’ sets, saving several moves);

(4) arrange the bottom layer corners into the correct places (ABA’B’ move set, once or twice, depending on how well you can read ahead)

(5) rotate the bottom layer corners in place (more A B A’ B’ sets, two or three times, four if you read the initial configuration wrongly).

Which is all very well and good. I got a 4-cube at the same time, and still can’t work out how to solve that.

Jerry, I noticed you have used

lagniappetwice in the last week. It’s nice to see that one of our less common Gulf coast words is making its way northward.I knew a kid in high school that could solve a Rubik’s cube behind his back while jumping on a pogo stick. People would bring him their own cubes, would mix the cubes up themselves, and then he’d jump on and go to work. Basically, he would find one cube (in the cube), keep track of it with his thumb, and finish the rest of it via mental mapping. He was pretty entertaining to watch.

His actual name is Ravi Fernando, a math student from Missouri, not Fernandez. He is juggling in front of the bookstore which is a fairly popular spot for Stanford jugglers (Down with Gravity, late Friday afternoons). When not juggling he can apparently solve a cube in about 10 seconds.

BTW he also got 8th in the 2011 Putnam Competition.

Solving a Rubik’s Cube is incredibly easy once you know how. You don’t even have to look at the thing except to see the starting position on one side. Once you know that, the speed of solving the cube is based only on how fast you can turn the sides. When I was in high school I could solve the cube in about 20 seconds with my eyes closed. Admittedly I found the solution in a book and didn’t solve it on my own, but I sure impressed the hell out of people.

I would bet very few (probably none) of the speed solvers of the rubiks cube actually solved it on their own. I read the solution myself. Basically it’s a memorization of moves based on pattern. I never memorized the complete pattern. I solve the first layer brute force first, which is easy. Then the 2nd layer is solved by applying memorized pattern after trying to put the cubes in certain patterns. The last layer is purely solved by memorized sequence of moves.

My brother and his friends worked on speed solving. I made patterns. Now I have three cubes, one normal, one with a twisted corner and one with two sides reversed so I can get patterns that are not available on a regular cube. I also have 2 x 2, 4 x 4 and 5 x 5 cubes. Eventually I will splurge and get the 6 x 6 and 7 x 7 cubes just to see what patterns I can make on those..And I cannot juggle worth a damn!

The “Piano Juggler” is not playing a piano or a keyboard in any sense. He isn’t. Sorry!!! Unless you mean something like a keyboard where you press one key and a whole melody comes out. Very impressive, not.

Though he seems like a nice enough fellow and he certainly wants to entertain the crowd from a good heart. So that’s a good thing.

I’d be amazed seeing a video of an actual concert pianist who can juggle. Or solve a scientific problem of any sort :-)

Igudesman

(and Joo):Well, in a more recent thread, Dr. Coyne shows a video of Harvard math professor Tom Lehrer, who is quite a decent pianist

(and competent vocalist, composer and lyricist). Does that qualify?Oh, and I am a concert pianist, and I can juggle

(the juggling part is reasonably easy, the piano playing is quite a bit more difficult).Here’s a female engineer/concert pianist/Rhodes Scholar:

http://engineeryourlife.weebly.com/2/post/2010/11/female-engineerconcert-pianistall-around-amazing-woman-takes-home-the-big-trophy-congrats-jennifer-lai.html

Or:

http://www-bcf.usc.edu/~echew/ahi/elaine_chew.html

Daniel Dennett put himself through college as a pianist.

LOTSof scientists are musicians.I doubt seriously that I could solve the Rubik’s cube today, but when I was a teenager, I regularly managed to get it back into its correct position within just a few minutes.

It was extremely easy. Anyone who wasn’t able to do so has a serious mental deficiency.

All you need to do is to take an ordinary kitchen knife and lever one of the pieces out. The remainder of the cube can then be easily disassembled and reassembled into the correct position.

The other way I did it was that I bought a book explaining how it was done, which I then modified. From memory, I realized that once I got one face correct, the remainder almost seemed to solve itself.

Ah. You’re not an engineer, by chance? ;)

Something I always regarded as being quite as remarkable as the complexity of the puzzle itself, was how the damn thing was made. Contemplate the problem of how to make three rows of squares slide past each other in any one of three planes, and the answer is not at all intuitive.

Can Ravi solve a Stanford woman? That’s the real puzzle.

;)

sub

The good old Rubik’s cube!

I could only ever get as far as solving 3 sides of it. :-)

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