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"8th of 7" cube toy

Renamed in honor of a prolific Halfbaker
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A toy in the form of a hollow cube with clear plastic walls, small enough to hold in your hand. Inside of this cube are 7 additional cubes half as large - leaving one empty cube-shaped space within. The inner cubes are metal (or have metal inserts) so the player can slide them around from outside using a magnet.

The inner cubes are printed with colors, numbers, or pictures on them, and players can scramble and re-arrange them any way they like.

Light years of fun for the whole collective. Keeps your little drones busy in the back pod - you won't have to listen to them whining "are we assimilated yet?" - for the whole trip.

kdf, May 18 2020

Like this, but in 3D https://en.wikipedia.org/wiki/15_puzzle
[kdf, May 18 2020]

Inspired by the prison in Smallworld https://books.googl...tml?id=UlAZj_d5vAoC
Dominic Green short story collection [kdf, May 18 2020]

Yongjun Spherical Magic Cube https://www.aliexpr...em/32794683472.html
A 3D slider puzzle using a different mechanism [xaviergisz, May 19 2020]

Matt Parker https://www.youtube.com/user/standupmaths
[Voice, May 20 2020]

Soviet Union Minus Cube http://www.twistypu...uzzle.cgi?pkey=1003
Here's a 2x2x2 version. [tatterdemalion, May 20 2020]

Other 3-d sliding block puzzles http://www.twistypu....cgi?act=mec&key=67
[tatterdemalion, May 20 2020]

Varikon 2 https://www.jaapsch...uzzles/varikon2.htm
Good overview of this kind of puzzle [kdf, May 20 2020, last modified May 21 2020]

MINUS CUBE https://en.wikipedia.org/wiki/Minus_Cube
The right Google search term takes you to Wikipedia [kdf, May 21 2020]

[link]






       Afterthought - Although I originally pictured it as an cube of 8 spaces (seven filled, one empty) ... like the prison in Dominic Green's "Smallworld" (link)... you could have one of any size. The next size up would be a cube of 27 spaces, 26 filled; then 64/63, and so on until it become unwieldy...   

       The smallest version would be relatively easy as you can see all of the pieces, only some of their faces would be obscured. The higher-order ones could be fiendishly difficult as you can't see any of the inside pieces at all until you move them to the perimeter...
kdf, May 18 2020
  

       To move the "inner" cubes, you would need each cube to contain a (good, polar) magnet; so you could "push" a whole row away. There is no other way to move the "inners", at least beyond 4th order (with 3rd & 4th order, you could move the gap then "pull" to the boundary).
neutrinos_shadow, May 19 2020
  

       Yes, I thought of the need to push cubes in any but the smallest model. Repelling magnets would be a problem though with so many adjacent pieces. Maybe the outer casing could be perforated to let you poke them with a stick.
kdf, May 19 2020
  

       The original name "Yet Another Cube Toy" just wasn't catchy enough. New name is fitting as the thing has 7 cubes in the space of 8 ... with the 8th part empty, like his head (soul, heart, cojones, whatever)...
kdf, May 19 2020
  

       Does it come with a voodoo doll miniature 8th inside so that you can chase him around using the cubes?
xenzag, May 19 2020
  

       xenzag, I hadn't thought of that but you certainly could. Might have to license it from Scott Adams though, as an 8th effigy would look a lot like Wally from the Dilbert comic strip.
kdf, May 19 2020
  

       I envision [MaxwellBuchanan] holding the cube up to the light and saying something to irritate the cube, just enough though, to make the afternoon interesting.
blissmiss, May 19 2020
  

       This must be a thing. Immediately.   

       <Starts to programme replicator/>   

       [+]   

       Oh, and we want royalties on every unit sold.   

       // soul //   

       Errr, what ? We can identify the other squishy organic bits, but what is "soul" ? Some sort of musical genre ?
8th of 7, May 19 2020
  

       Disliking the name change.   

       Would this be a extremely simple solve? Unlike a two dimensional Sam Loyd puzzle where you can only slide in the x/y, I'm picturing one with a z coordinate where it's an easy process to get a piece in its proper spot by moving it back and behind blocking pieces and then emerging on the other side. Multiply by 6 and you have your cube.   

       I don't have the maths or visualization skills to answer this properly.
tatterdemalion, May 19 2020
  

       "This must be a thing, immediately"
Seriously. I'm surprised it isn't. I looked online, couldn't find anything like it, thought one of the first annos would be somebody pointing to one. Maybe someone with better search skills can find one.
kdf, May 19 2020
  

       "disliking the name"
Beats calling it "Yet another cube toy" - got anything better? The name came to me when I was doing notations for higher order versions... 27/26, 64/63, and so on.
  

       "would this be extremely simple?"
Yes, I think 8th of 7 is extremely simple. Mindless entertainment and a fidgeting waste of time, at best ... Oh wait, did you mean the puzzle? Probably, I haven't done the math yet either. I think 27 and 64 would be a lot harder.
kdf, May 19 2020
  

       It could turn out to be one of those math oddities where it is either so simple it doesn't justify existence, or it's absolutely impossible. I bet Matt Parker would know (or would find out).   

       Better name? Literally anything else, but start with KDF cube.
tatterdemalion, May 19 2020
  

       Well, as long as you're keeping it as 2x2x2, you can rotate instead of translate.
FlyingToaster, May 19 2020
  

       Should be trivial to calculate the number of permutations.   

       7 cubes in 8 spaces... surely there's 8! possible configurations? i.e.40320   

       A 3x3x3 puzzle has 27 spaces and 26 cubes. 27! possible configurations is 10888869450418352160768000000 which is a bit more of a challenge.   

       The other thing about 3x3x3 cubes is that the space has limitations on how it can be moved. You could use a push stick to push rows of cubes, but that limits you to having the space in the corners. Using a magnet to drag cubes would let you drag a cube into the corner, shifting the space to the centre of an edge; you could also drag the cube from the centre of a face to the edge to shift the space to the centre of the face. You could then hold the cube in the centre of the opposite face up with the magnet, and turn the whole thing to let the cube in the centre fall to the opposite face, moving the space to the true centre of the whole cube.   

       For a 4x4x4 cube (64 spaces, 63 cubes, 64! permutations i.e. approximately 1.268869321 E+89), the magnet + gravity trick would allow you to shift the space to any of the 64 spaces. But in a 5x5x5 cube (125 spaces, 124 cubes, 125! permutations, i.e. approx. 1.882677176 E+209), you would not be able to move the space into the exact centre of the cube unless you had a double-strength magnet able to hold two stacked cubes against gravity. And similarly for higher numbers.
pocmloc, May 19 2020
  

       Postulation: [pocmloc] is Matt Parker IRL.   

       Discuss.
Sgt Teacup, May 19 2020
  

       I had considered that possibility.
tatterdemalion, May 19 2020
  

       //Matt Parker// never heard of him, sorry. Nice try though.
pocmloc, May 20 2020
  

       That's just the sort of thing the real Matt Parker would say.
tatterdemalion, May 20 2020
  

       // "This must be a thing, immediately" // Seriously. I'm surprised it isn't.   

       Ah well there you go. Looks like TwistyPuzzles site has you covered. (links)
tatterdemalion, May 20 2020
  

       "TwistyPuzzles"
Good find, thanks! Now that I know the right search phrases I see there are lots of good links. One of them (Varikon2 link) mentions Piet Hein invented one of the earliest versions. This delights but does not surprise me as I'm already familiar with some of his other creations.
kdf, May 20 2020
  

       //Matt Parker// Spiderman ?
FlyingToaster, May 20 2020
  

       Doubleplusgood [+]
21 Quest, May 21 2020
  

       Could a designed network of magnetic poles be the puzzle? Sliding across a face would take some energy but row pushing same poles or pulling different ones would be the puzzle move to avoid.
wjt, May 23 2020
  
      
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