A new take on cubing -No colors, just numbers!!

[jwilde0926]

Hey SpeedSolving!

My name’s James and I’m writing to you on behalf of the Innovation Factory in Chicago. We’re launching a product called the Magic Cube that I think you guys are really going to like. It takes the traditional 3x3x3 Rubik’s Cube and adds a layer of complexity. We've determined six significant number sequences and constants and arranged each of them on a side of the cube. It's your task to not only discover the arrangement of numbers on each face, but to rearrange them so that they are in the correct order and orientation.

We believe this is an extremely difficult, bordering on insane task, but figured that if anyone could solve it, this would be a great place to start. To find someone able to accomplish this, we’ve launched a competition to see who can solve it first. We’ve sent out invitations to high-ranking geniuses that we think have a shot at it, but have also opened it up to anyone to nominate themself or someone else. If selected, you will receive a free plastic version of the Magic Cube and the first person to correctly solve it will receive one of the first solid aluminum, engraved Magic Cubes.

If you would like to nominate yourself or someone else, please send an email to [email protected] with the following info:

Name of Nominee:
Email of Nominee:
(Include your name and email if you are nominating someone else)
Shipping Address of Nominee:
Reason why you think Nominee is worthy of this challenge:

For more info, check out our product page at http://if-chicago.com/portfolio/the-magic-cube and watch the video on that page and at http://youtu.be/hmbthzn7qqc

Happy Cubing!

 

[Mike Hughey]

If the numbers really have to be oriented correctly so that they face up, the number of possible solutions once you solve the cube for orientation is really quite small. I'm guessing one of our math whiz people here can surely solve it easily within hours of receiving it. qqwref, cmhardw, Tim Reynolds, cuBerBruce - I'd think any of them would have an easy time with this.

Would anyone care to calculate the number of possible solutions given correct orientation, just so we know just how hard this really might be?

 

[Wassili]

Wait, I'm confused, how does the cube look like in a solved state?

 

[Mike Hughey]

If you watch the video, it implies that the solved state will have a set of numbers all facing the same direction on each face. The numbers on any given face will form some sequence that makes some kind of sense. Since the OP talks about number sequences and constants, I'm guessing that each face is probably either a mathematical sequence of some sort or else digits from some well-known constant, like maybe pi or e.

 

[Wassili]

Ah yes, sorry I missed the video!

 

[Mike Hughey]

I guess this is harder than I thought. For each layer, bottom, middle, top, all pieces of a given type (corners or edges) could be exchanged, although that would be constrained by parity. So is that (24 ^ 5) / 2 possibilities? So about 4 million. I guess how hard this is would depend on how obvious the sequences and/or constants are to identify, and maybe on a bit of luck stumbling on the answer.

Perhaps the way to solve this would be to first solve the cube for orientation, then write a program to generate the 4 million combinations, then start looking through the generated list trying to find a combination that makes sense? If you had a program that looked for sequences/constants, that might help.

 

[Stefan]

Is someone willing to provide the layout? Brest?

Spoiler

Mike: I'm pretty sure I've seen 13, 21, 34 possible as a bottom row. That should pretty much tell us one layer, reduce the number of possibilities, and give us hints for the adjacent layers.

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Quote from the video: "That's around 3000 times as many combinations as for a regular Rubik's cube. So it's a great deal more difficult."

Hahahahahahahaha. Hahahahahahahahahahahahaha. No.

Also, "magic cube"? You pick the generic name used by knock-offs as the name for your product?

 

[Nathan Dwyer]

"Magic Cube" = terribly generic name

 

[Mike Hughey]

I guess this is harder than I thought. For each layer, bottom, middle, top, all pieces of a given type (corners or edges) could be exchanged, although that would be constrained by parity. So is that (24 ^ 5) / 2 possibilities? So about 4 million. I guess how hard this is would depend on how obvious the sequences and/or constants are to identify, and maybe on a bit of luck stumbling on the answer.

Perhaps the way to solve this would be to first solve the cube for orientation, then write a program to generate the 4 million combinations, then start looking through the generated list trying to find a combination that makes sense? If you had a program that looked for sequences/constants, that might help.

Wait, I'm stupid. If the numbers are all facing up on the 4 sides when it's solved (which looks likely based on watching the video, although I'm not positive of it), then there really is only one possible configuration for the top and bottom faces. (Unless you count some of the numbers which could face either way, like 6 vs. 9. And that won't make it that much harder unless there are a lot of them, and it doesn't look like there are.) So that brings our 4 million down to ... 24. Wow. This is going to be solved almost instantly. (If my assumptions are correct.)

 

[j0k3rj0k3r]

I think the magic cube is a play off of magic squares which are here

 

[Stefan]

I might know three sides now.

Spoiler: last three numbers on the three sides

_, _, _, _, _, _, 13, 21, 34

Spoiler: name of sequence

Fibonacci numbers

_, _, _, _, _, _, 28, 36, 45

Spoiler: name of sequence

Triangular numbers

_, _, _, _, _, _, 17, 19, 23

Spoiler: name of sequence

Prime numbers

And j0k3rj0k3r might be "right", one side could be the standard magic square ("right" in quotes cause that's not quite what he said). I think so because there are at least two "5" centers, because there's at least one lower right "2" so not all will be increasing sequences, and because there really should be a magic square side.

 

[420]

I, for one, think that this is a pretty damn cool looking puzzle. Some of the math whizzes on here could just plug a bunch of numbers into some magical equation of theirs and solve this almost immediately, but to actually experiment and identify the significance of the numbers seems like quite a challenge for somebody like myself with not as much mathematical knowledge of the cube.

Question, though. I'm assuming that, since this is a sort of competition, the cubes will all be mailed out pre-"scrambled"?

It'd be extremely fun to have a puzzle like this, though, knowing that you'd be pitted against some of the most intellectual people on the planet to solve it.

Good luck to anybody who undertakes the challenge!

 

[Stefan]

the cubes will all be mailed out pre-"scrambled"?

Obviously. Also, they kinda said something like that in the video.

It'd be extremely fun to have a puzzle like this, though, knowing that you'd be pitted against some of the most intellectual people on the planet to solve it.

They're trying to give them to company CEOs/bosses, not Stephen Hawking.

 

[420]

Obviously. Also, they kinda said something like that in the video.

They're trying to give them to company CEOs/bosses, not Stephen Hawking.

My apologies, wasn't able to watch the video with sound yet; was only able to glance through it briefly.

*Correction: the people who work with the most intellectual people on the planet but who aren't quite them.*

 

[Stefan]

*Correction: the people who work with the most intellectual people on the planet but who aren't quite them.*

And I admit they at least went on saying "heads of math departments", cryptologists and former hackers (why *former*?).

 

[Owen]

former hackers (why *former*?).

I'd guess it's because "hacking" is seen by the media as illicit or criminal.

 

[420]

I'd guess it's because "hacking" is seen by the media as illicit or criminal.

Well, there's something called "ethical hacking". Although the fact that they needed to include the word "former" probably hints at the fact that they weren't ethical hackers. The fact that we know exactly who these people are probably hints that they weren't very good "unethical hackers" either.

 

[flee135]

This reminds me of a sudokube. I bought one before I knew how to solve Rubik's Cubes, but shortly after I learned how to solve one, it wasn't too hard to use that knowledge to solve one. Based on how the corners looked, I could tell that four of the centers were all oriented in the same direction, so just based on the orientation of some of the numbers, it's easy to figure out where the pieces need to go. The thing with the sudokube is that it wasn't hard to verify that a piece is in the wrong place (no two digits on a side can be the same), which might be a little tougher for this puzzle, but on the other hand, as you get more pieces in place, it shouldn't be hard to recognize some of the sequences and constants on this puzzle either.

 

[windhero]

Isnt this just a sudokube with a bit more trial and error involved? I dont think this is anything new in the range of difficulty. Just orient everything correctly and figure out the order, no?

 

[windhero]

Here are some of the pieces I saw, I'm not 100% sure. But yeah, if you orient all the corners and all the centers it doesnt leave many choices now does it?

Edges:
8-1
21-X
3-13
8-X
6-3
4-3
1-16
7-X


Corners:
6-5-2
5-x-x
17-3-x
1-10-x
34-x-x
2-2-x
1-1-38
13-2-8

These 2 are a combination with the above, didnt see all the number at once so it has to be deduced without seeing it)
28-x-x
4-45-x
Centers
5
11
15
2